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Topological spaces with the Freese--Nation property IIApr 18 2019The aim of this paper is to study the class of spaces with the FNS property and $\pi-\FNS$ property. We shown that compact spaces with the FNS property for some base consisting of cozero-sets are openly generated spaces and spaces with the $\pi-\FNS$ ... More

Spaces of max-min measures on compact Hausdorff spacesApr 18 2019The notion of max-min measure is a counterpart of the notion of max-plus measure (Maslov measure or idempotent measure). In this paper we consider the spaces of max-min measures on the compact Hausdorff spaces. It is proved that the obtained functor of ... More

On Loeb and sequential spaces in $\mathbf{ZF}$Apr 14 2019A topological space is called Loeb if the collection of all its non-empty closed sets has a choice function. In this article, in the absence of the axiom of choice, connections between Loeb and sequential spaces are investigated. Among other results, ... More

On $p$-compact group topologies on direct sums of ${\mathbb Q}$Apr 11 2019We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(\kappa)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $\kappa =\kappa^\omega$. In particular, this gives the first arbitrarily ... More

Sheaves and DualityApr 11 2019It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a generalisation of this ... More

The distribution function of a probability measure on a linearly ordered topological spaceApr 11 2019In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case. Moreover, we define ... More

Stochastic Comparative Statics in Markov Decision ProcessesApr 10 2019In multi-period stochastic optimization problems, the future optimal decision is a random variable whose distribution depends on the parameters of the optimization problem. We analyze how the expected value of this random variable changes as a function ... More

Countable dense homogeneity of function spacesApr 09 2019In this paper we consider the question of when the space $C_p(X)$ of continuous real-valued functions on $X$ with the pointwise convergence topology is countable dense homogeneous. In particular, we focus on the case when $X$ is countable with a unique ... More

Dispersion points, indecomposable connected sets, and rational continuaApr 09 2019We construct a biconnected set with a dispersion point which can be embedded into a rational continuum. The example possibly answers a question by Joachim Grispolakis. It generates an indecomposable connected plane set which also embeds into a rational ... More

Dispersion points, indecomposable connected sets, and rational continuaApr 09 2019Apr 16 2019We construct a biconnected set with a dispersion point which can be embedded into a rational continuum. The example possibly answers a question by Joachim Grispolakis. It generates an indecomposable connected plane set which also embeds into a rational ... More

Dispersion points, indecomposable connected sets, and rational continuaApr 09 2019Apr 21 2019We construct a biconnected set with a dispersion point which can be embedded into a rational continuum. The example possibly answers a question by Joachim Grispolakis. It generates an indecomposable connected plane set which also embeds into a rational ... More

Pseudoradial spaces and copies of $ω_1+1$Apr 09 2019In this paper we compare the concepts of pseudoradial spaces and the recently defined strongly pseudoradial spaces in the realm of compact spaces. We show that $\mathrm{MA}+\mathfrak{c}=\omega_2$ implies that there is a compact pseudoradial space that ... More

Enumeration degrees and non-metrizable topologyApr 08 2019The enumeration degrees of sets of natural numbers can be identified with the degrees of difficulty of enumerating neighborhood bases of points in a universal second-countable $T_0$-space (e.g. the $\omega$-power of the Sierpi\'nski space). Hence, every ... More

Conley index approach to sampled dynamicsApr 07 2019The topological method for the reconstruction of dynamics from time series [K. Mischaikow, M. Mrozek, J. Reiss, A. Szymczak. Construction of Symbolic Dynamics from Experimental Time Series, Physical Review Letters, 82 (1999), 1144-1147] is reshaped to ... More

Conceptual proofs of the Menger and Rothberger gamesApr 04 2019We provide conceptual proofs of the two most fundamental theorems concerning topological games and open covers: Hurewicz's Theorem concerning the Menger game, and Pawlikowski's Theorem concerning the Rothberger game.

Eulerian SpacesApr 04 2019We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and K\"uhn with the topological theory of Eulerian continua defined as irreducible images of the ... More

Pairwise Semiregular Properties on Generalized Pairwise Lindelof SpacesApr 04 2019Let $\left( X,\tau _{1},\tau _{2}\right) $ be a bitopological space and $% \left( X,\tau _{\left( 1,2\right) }^{s},\tau _{\left( 2,1\right) }^{s}\right) $ its pairwise semiregularization. Then a bitopological property $\mathcal{P}$\ is called pairwise ... More

Loop Homology of Bi-secondary StructuresApr 03 2019In this paper we compute the loop homology of bi-secondary structures. Bi-secondary structures were introduced by Haslinger and Stadler and are pairs of RNA secondary structures, i.e. diagrams having non-crossing arcs in the upper half-plane. A bi-secondary ... More

An Embedding Lemma in Soft Topological SpacesApr 02 2019In 1999, Molodtsov initiated the concept of Soft Sets Theory as a new mathematical tool and a completely different approach for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the theory of ... More

Continuous Selections of Lower semicontinuous Set-valued MappingsApr 01 2019A space $X$ is strongly $Y$-selective (resp., $Y$-selective) if every lower semicontinuous mapping from $Y$ to the nonempty subsets (resp., nonempty closed subsets) of $X$ has a continuous selection. We also call $X$ (strongly) $C$-selective if it is ... More

Hausdorffness of General CompactificationsMar 31 2019Magill proved that the remainders of two locally compact Hausdorff spaces in their StoneCech compactifications are homeomorphic if and only if the lattices of their Hausdorff compactifications are lattice isomorphic. His construction for compactifications ... More

Twisted Coefficients on coarse Spaces and their CoronaMar 31 2019To a metric space $X$ we associate a compact topological space $\nu' X$ called the corona of $X$. Then a coarse map $f:X\to Y$ between metric spaces is mapped to a continuous map $\nu' f:\nu' X\to \nu' Y$ between coronas. Sheaf cohomology on coarse spaces ... More

Notes on the tightness of $G_δ$-modificationsMar 31 2019We construct a countably tight normal $T_1$ space $X$ with $t(X_\delta) >2^\omega$. This is an answer to the question posed by Dow-Juh\'asz-Soukup-Szentmikl\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_\delta$-modifications ... More

$σ$-Continuous functions and related cardinal characteristics of the continuumMar 30 2019Apr 02 2019A function $f:X\to Y$ between topological spaces is called $\sigma$-$continuous$ (resp. $\bar\sigma$-$continuous$) if there exists a (closed) cover $\{X_n\}_{n\in\omega}$ of $X$ such that for every $n\in\omega$ the restriction $f{\restriction}X_n$ is ... More

Parametric identification of the dynamics of inter-sectoral balance: modelling and forecastingMar 29 2019This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identification of a weakly formalized dynamical system is developed. A matching ... More

Simple way to prove compactness of closed intervals in simply ordered set with order topologyMar 29 2019In this note, we present a simpler way to prove the compactness of the closed intervals in simply ordered set with order topology.

Microbundles over topological ringsMar 27 2019The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are investigated.

Estimation of the Shapley Value of a Peer-to-Peer Energy Sharing Game using Coalitional Stratified Random SamplingMar 26 2019Various peer-to-peer energy markets have emerged in recent years in an attempt to manage distributed energy resources in a more efficient way. One of the main challenges these models face is how to create and allocate incentives to participants. Cooperative ... More

Improving the Scalability of a Prosumer Cooperative Game with K-Means ClusteringMar 26 2019Among the various market structures under peer-to-peer energy sharing, one model based on cooperative game theory provides clear incentives for prosumers to collaboratively schedule their energy resources. The computational complexity of this model, however, ... More

Cantor's intersection theorem in the setting of $\mathcal{F}$-metric spacesMar 24 2019This paper deals with an open problem posed by Jleli and Samet in \cite[\, M.~Jleli and B.~Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl, 20(3) 2018]{JS1}. In \cite[\, Remark 5.1]{JS1} They asked whether the Cantor's intersection ... More

Baire category properties of function spaces with the Fell hypograph topologyMar 24 2019For a Tychonoff space $X$ and a subspace $Y\subset\mathbb R$, we study Baire category properties of the space $C_{\downarrow F}(X,Y)$ of continuous functions from $X$ to $Y$, endowed with the Fell hypograph topology. We characterize pairs $X,Y$ for which ... More

Precompact groups and convergenceMar 21 2019We consider precompact sequential and Fr\'echet group topologies and show that some natural constructions of such topologies always result in metrizable groups answering a question of D.~Dikranjan et al. We show that it is consistent that all sequential ... More

Spaces of small cellularity have nowhere constant continuous images of small weightMar 20 2019We call a continuous map $f : X \to Y$ nowhere constant if it is not constant on any non-empty open subset of its domain $X$. Clearly, this is equivalent with the assumption that every fiber $f^{-1}(y)$ of $f$ is nowhere dense in $X$. We call the continuous ... More

Selection principles and games in bitopological function spacesMar 19 2019For a Tychonoff space $X$, we denote by $(C(X), \tau_k, \tau_p)$ the bitopological space of all real-valued continuous functions on $X$ where $\tau_k$ is the compact-open topology and $\tau_p$ is the topology of pointwise convergence. In papers [5, 6, ... More

Countably compact groups and sequential orderMar 19 2019We use $\diamondsuit$ to construct, for every $\alpha\leq\omega_1$ a sequential countably compact topological group of sequential order $\alpha$. This establishes the independence of the existence of sequential countably compact non Fr\'echet groups from ... More

Algebras of the extended probabilistic powerdomain monadMar 18 2019We investigate the Eilenberg-Moore algebras of the extended probabilistic powerdomain monad $\mathcal V_w$ over the category $\mathbf{TOP}_0$ of $T_0$ topological spaces and continuous maps. We prove that every $\mathcal V_w$-algebra in our setting is ... More

Algebras of the extended probabilistic powerdomain monadMar 18 2019Mar 22 2019We investigate the Eilenberg-Moore algebras of the extended probabilistic powerdomain monad $\mathcal V_w$ over the category $\mathbf{TOP}_0$ of $T_0$ topological spaces and continuous maps. We prove that every $\mathcal V_w$-algebra in our setting is ... More

Algebras of the extended probabilistic powerdomain monadMar 18 2019Mar 19 2019We investigate the Eilenberg-Moore algebras of the extended probabilistic powerdomain monad $\mathcal V_w$ over the category $\mathbf{TOP}_0$ of $T_0$ topological spaces and continuous maps. We prove that every $\mathcal V_w$-algebra in our setting is ... More

On Baire category properties of function spaces $C_k'(X,Y)$Mar 17 2019We prove that for a stratifiable scattered space $X$ of finite scattered height, the function space $C_k(X)$ endowed with the compact-open topology is Baire if and only if $X$ has the Moving Off Property of Gruenhage and Ma. As a byproduct of the proof ... More

A criterion for the triviality of the centralizer for vector fields and applicationsMar 17 2019In this paper we establish a criterion for the triviality of the $C^1$-centralizer for vector fields and flows. In particular we deduce the triviality of the centralizer at homoclinic classes of $C^r$ vector fields ($r\ge 1$). Furthermore, we show that ... More

Comparing topologies on the Morse boundary and quasi-isometry invarianceMar 17 2019We compare several topologies on the Morse boundary $\partial_M Y$ of a $\mathrm{CAT}$ cube complex $Y$. In particular, we show that the two topologies introduced by Cashen and Mackay are not equal in general and provide a new description of one of them ... More

Comparing topologies on the Morse boundary and quasi-isometry invarianceMar 17 2019Mar 22 2019We compare several topologies on the Morse boundary $\partial_M Y$ of a $\mathrm{CAT(0)}$ cube complex $Y$. In particular, we show that the two topologies introduced by Cashen and Mackay are not equal in general and provide a new description of one of ... More

Shortest paths in arbitrary plane domainsMar 15 2019Let $\Omega$ be a connected open set in the plane and $\gamma: [0,1] \to \overline{\Omega}$ a path such that $\gamma((0,1)) \subset \Omega$. We show that the path $\gamma$ can be ``pulled tight'' to a unique shortest path which is homotopic to $\gamma$, ... More

Quasi-uniform type spacesMar 15 2019In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's theory of partial ... More

On generalization of theorems of PestriakovMar 14 2019In 1987 A.V. Pestriakov proved a series of theorems for cardinal functions of the space $B_{\alpha}(X)$ of all real-valued functions of Baire class $\alpha$ $(\alpha> 0)$, and he conjectured that most of these theorems are true for spaces containing all ... More

Products of Luzin-type sets with combinatorial propertiesMar 12 2019We construct Luzin-type subsets of the real line in all finite powers Rothberger, with a non-Menger product. To this end, we use a purely combinatorial approach which allows to weaken assumptions used earlier to construct sets with analogous properties. ... More

Sequential coarse structures of topological groupsMar 10 2019We endow a topological group $(G, \tau)$ with a coarse structure defined by the smallest group ideal $S_{\tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{\tau})$. If $G$ is discrete then ... More

Sequential coarse structures of topological groupsMar 10 2019Mar 19 2019We endow a topological group $(G, \tau)$ with a coarse structure defined by the smallest group ideal $S_{\tau} $ on $G$ containing all converging sequences with their limits and denote the obtained coarse group by $(G, S_{\tau})$. If $G$ is discrete then ... More

Finite powers and products of Menger setsMar 07 2019We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in the Blass--Shelah ... More

Returning functions with closed graph are continuousMar 05 2019A function $f:X\to \mathbb R$ defined on a topological space $X$ is called returning if for any point $x\in X$ there exists a positive real number $M_x$ such that for every path-connected subset $C_x\subset X$ containing the point $x$ and any $y\in C_x\setminus\{x\}$ ... More

Proximity inductive dimension and Brouwer dimension agree on compact Hausdorff spacesMar 04 2019In this paper we show that the proximity inductive dimension defined by Isbell agrees with the Brouwer dimension originally described by Brouwer on the class of compact Hausdorff spaces. Consequently, Fedorchuk's example of a compact Hausdorff space whose ... More

Locally small spaces with an applicationMar 03 2019We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

Strong homotopy of digitally continuous functionsMar 02 2019We introduce a new type of homotopy relation for digitally continuous functions which we call ``strong homotopy.'' Both digital homotopy and strong homotopy are natural digitizations of classical topological homotopy: the difference between them is analogous ... More

A functional representation of the capacity multiplication monadMar 02 2019Functional representations of the capacity monad based on the max and min operations were considered in \cite{Ra1} and \cite{Ny1}. Nykyforchyn considered in \cite{Ny2} some alternative monad structure for the possibility capacity functor based on the ... More

A complete Heyting algebra whose Scott space is non-soberMar 02 2019We prove that (1) for any complete lattice $L$, the set $\mathcal{D}(L)$ of all nonempty saturated compact subsets of the Scott space of $L$ is a complete Heyting algebra (with the reverse inclusion order); and (2) if the Scott space of a complete lattice ... More

Graded topological spacesFeb 28 2019We introduce the notion of a "graded topological space": a topological space endowed with a sheaf of abelian groups which we think of as a sheaf of gradings. Any object living on a graded topological space will be graded by this sheaf of abelian groups. ... More

Domain-complete and LCS-complete spacesFeb 28 2019We study $G_\delta$ subspaces of continuous dcpos, which we call domain-complete spaces, and $G_\delta$ subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those include all locally compact sober spaces-in particular, all continuous ... More

On the monotonicity of the eigenvector methodFeb 27 2019Pairwise comparisons are used in a wide variety of decision situations when the importance of different alternatives should be measured by numerical weights. One popular method to derive these priorities is based on the right eigenvector of a multiplicative ... More

Mean-field moral hazard for optimal energy demand response managementFeb 27 2019We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a mean-field of consumers, whose consumption is impacted by a common noise. We formulate the problem as a Principal-Agent problem with moral ... More

Mean-field moral hazard for optimal energy demand response managementFeb 27 2019Mar 14 2019We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a mean-field of consumers, whose consumption is impacted by a common noise. We formulate the problem as a Principal-Agent problem with moral ... More

On some functional generalizations of the regularity of topological spacesFeb 26 2019We introduce and study some generalizations of regular spaces, which were motivated by studying continuity properties of functions between (regular) topological spaces. In particular, we prove that a first-countable Hausdorff topological space is regular ... More

A lower density operator for the Borel algebraFeb 26 2019We prove that the existence of a Borel lower density operator (a Borel lifting) with respect to the $\sigma$-ideal of countable sets, for an uncountable Polish space, is equivalent to the Continuum Hypothesis.

Ekeland, Takahashi and Caristi principles in quasi-pseudometric spacesFeb 26 2019We prove versions of Ekeland, Takahashi and Caristi principles in sequentially right $K$-complete quasi-pseudometric spaces (meaning asymmetric pseudometric spaces), the equivalence between these principles, as well as their equivalence to the completeness ... More

Ekeland, Takahashi and Caristi principles in quasi-pseudometric spacesFeb 26 2019Mar 09 2019We prove versions of Ekeland, Takahashi and Caristi principles in sequentially right $K$-complete quasi-pseudometric spaces (meaning asymmetric pseudometric spaces), the equivalence between these principles, as well as their equivalence to the completeness ... More

Ideals in $B_1(X)$ and residue class rings of $B_1(X)$ modulo an idealFeb 24 2019This paper explores the duality between ideals of the ring $B_1(X)$ of all real valued Baire one functions on a topological space $X$ and typical families of zero sets, called $Z_B$-filters, on $X$. As a natural outcome of this study, it is observed that ... More

On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finite singular valuesFeb 23 2019Mar 15 2019The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of inverse images such that the set of all vertices coincides with the set of all connected components of inverse images including singular ... More

On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finite singular valuesFeb 23 2019The Reeb graph of a function on a smooth manifold is the graph obtained as the space of all connected components of inverse images such that the set of all vertices coincides with the set of all connected components of inverse images including singular ... More

A metrizable semitopological semilattice with non-closed partial orderFeb 23 2019We construct a metrizable semitopological semilattice $X$ whose partial order $P=\{(x,y)\in X\times X:xy=x\}$ is a non-closed dense subset of $X\times X$. As a by-product we find necessary and sufficient conditions for the existence of a (metrizable) ... More

Nearness PosetsFeb 21 2019We extend nearness frames to posets representing bases and even subbases of $T_1$ spaces. This allows us to put a classic duality due to Wallman, between compact $T_1$ spaces and abstract simplicial complexes, into a general nearness framework. Within ... More

Long colimits of topological groups I: Continuous maps and homeomorphismsFeb 18 2019The union of a directed family of topological groups can be equipped with two noteworthy topologies: the finest topology making each injection continuous, and the finest group topology making each injection continuous. This begs the question of whether ... More

A 0-dimensional, Lindelöf space that is not strongly DFeb 18 2019A topological space $X$ is strongly $D$ if for any neighbourhood assignment $\{U_x:x\in X\}$, there is a $D\subseteq X$ such that $\{U_x:x\in D\}$ covers $X$ and $D$ is locally finite in the topology generated by $\{U_x:x\in X\}$. We prove that $\diamondsuit$ ... More

The congruence biframe as a quasi-uniform bicompletionFeb 17 2019K\"unzi and Ferrario have shown that a $T_0$ space is sober if and only if it is bicomplete in the well-monotone quasi-uniformity. We prove a pointfree version of this result: a strictly zero-dimensional biframe is a congruence biframe if and only if ... More

On quasi $κ$-metrizable spacesFeb 17 2019The aim of this paper is to investigate the class of quasi $\kappa$-metrizable spaces. This class is invariant with respect to arbitrary products and contains Schepin's $\kappa$-metrizable spaces as a proper subclass.

Between homeomorphism type and Tukey typeFeb 16 2019Call a compact space $X$ pin homogeneous if every two points $a,b$ are pin equivalent, meaning that there exists a compact space $Y$, a quotient map $f\colon Y\to X$, and a homeomorphism $g\colon Y\to Y$ such that $gf^{-1}\{a\}=f^{-1}\{b\}$. We will prove ... More

Alexander and Jones polynomials of surgerized tst linksFeb 15 2019Feb 19 2019This paper is a continuation on the 2012 paper on "Cutting Twisted Solid Tori (TSTs)", in which we considered twisted solid torus links (tst links). We generalize the notion of tst links to "surgerized tst links": recall that when performing $\Phi^\mu(n(\tau), ... More

Alexander and Jones polynomials of surgerized tst linksFeb 15 2019Feb 18 2019This paper is a continuation on the HLMA paper published in 2012 on twisted solid torus links (tst links). We generalize the notion of tst links to "surgerized tst links": recall that when performing $\Phi^\mu(n(\tau), d(\tau), M)$ on a tst $\langle \tau ... More

Some Properties of Thinness and Fine Topology with Relative CapacityFeb 14 2019In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely closed sets. We ... More

Overt choiceFeb 14 2019We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice ... More

Quantum computing, Seifert surfaces and singular fibersFeb 13 2019The fundamental group $\pi_1(L)$ of a knot or link $L$ may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, ... More

Constructing Selections Stepwise Over Cones of Simplicial ComplexesFeb 08 2019It is given a simplified proof of a natural generalisation of Uspenskij's selection characterisation of paracompact $C$-spaces. The method is also applied to give a simplified proof of a similar characterisation of paracompact finite $C$-space. Another ... More

A new characterization of partial metric completenessFeb 08 2019In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.

Partial quasi-metric completeness via Kannan-type fixed pointsFeb 08 2019In this short note, we obtain partial quasi-metric versions of Kannan's fixed point theorem for self-mappings. Moreover, we use these fixed points results to characterize a certain type of completeness in partial quasi-metric spaces. We have reported ... More

Chatterjea type fixed point in Partial $b$-metric spacesFeb 08 2019In this paper, we give and prove two Chatterjea type fixed point theorems on partial $b$-metric space. We propose an extension to the Banach contraction principle on partial $b$-metric space which was already presented by Shukla and also study some related ... More

An approach to harmonic analysis on non-locally compact groups I: level structures over locally compact groupsFeb 08 2019We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's Theorem) for such ... More

Two-Step market clearing for local energy trading in feeder-based marketsFeb 07 2019Recent innovations in Information and Communication Technologies (ICT) provide new opportunities and challenges for integration of distributed energy resources (DERs) into the energy supply system as active market players. By increasing integration of ... More

Deficient topological measures on locally compact spacesFeb 07 2019Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set function on ... More

Coarse structures on groups defined by $T$-sequencesFeb 06 2019A sequence $(a_{n}) $ in an Abelian group is called a $T$-sequence if there exists a Hausdorff group topology on $G$ in which $(a_{n}) $ converges to $0$. For a $T$-sequence $(a_{n}) $, $\tau_{(a_{n}) } $ denotes the strongest group topology on $G$ in ... More

Finite Topology on Shapes without PointsFeb 05 2019This paper develops finite topology on shapes formed with elements of the algebras $U_i$, for $i$ > 0. In traditional branches of topology, "shapes" are considered as abstract/immaterial objects, as subsets of an ambient space (e.g. Euclidean space) from ... More

Solid-set functions and topological measures on locally compact spacesFeb 05 2019A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all works devoted ... More

Topological Extensions of Rough Approximation SpacesFeb 05 2019In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of approximations ... More

Hyperballeans of groupsFeb 04 2019In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If $G$ is a group, we denote by $L(G)$ the family of all subgroups of $G$. For two groups ... More

Balleans, hyperballeans and idealsFeb 04 2019A ballean $\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of subsets of $X$ called balls (or entourages of the diagonal in $X\times X$) defined in such a way that $\mathcal{B}$ can be considered as the asymptotic counterpart of a uniform ... More

Products of elements of cobordism-like modules induced from generic mapsFeb 03 2019Recently the author has introduced cobordism-like modules induced from generic maps whose codimensions are negative. They are generalizations of cobordism modules of manifolds. They have been introduced in generalizing the following theorem shown by Hiratuka ... More

SSGP topologies on free groups of infinite rankFeb 03 2019We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity of G, each element g in G can be represented as a product g=g_1 g_2 ... ... More

Some Enumeration Problems in the Duplication-Loss Model of Genome RearrangementFeb 01 2019Tandem-duplication-random-loss (TDRL) is an important genome rearrangement operation studied in evolutionary biology. This paper investigates some of the formal properties of TDRL operations on the symmetric group (the space of permutations over an $ ... More

Adaptive Monte Carlo Multiple Testing via Multi-Armed BanditsFeb 01 2019Feb 19 2019Monte Carlo (MC) permutation test is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large number of hypothesis ... More

Adaptive Monte Carlo Multiple Testing via Multi-Armed BanditsFeb 01 2019Monte Carlo (MC) permutation testing is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large number of ... More

Fixed point sets in digital topology, 1Jan 30 2019In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often ... More

On the space of ends of infinitely generated groupsJan 30 2019We study the space of ends of groups. For a finitely generated group, this is a Cantor space as soon as it is infinite. In contrast, we show that for infinitely generated countable groups, it exhibits several behaviors. For instance, we show that for ... More

The cometrizability of generalized metric spacesJan 30 2019Feb 05 2019A topological space $X$ is cometrizable if it admits a weaker metrizable topology such that each point $x\in X$ has a (not necessarily open) neighborhood base consisting of metrically closed sets. We prove that the class of cometrizable spaces includes ... More