一般拓扑

In this paper, we extend the notion of directed clique complex to quivers and introduce an associated homology theory. By applying this construction to biquandle coloring quivers, we obtain new invariants of links. We then introduce a…

This short paper is a small contribution to the field of Boolean contact algebras. We analyze the nondefinability of the property of interior-connectedness, and we prove certain minimality conditions for algebras and spaces that can be used…

In this paper,we introduce the concept of GSI$_2$-convergence in $T_0$ spaces and the related concept of (strongly) QI$_2$-continuous spaces. It is proved that if GSI$_2$-convergence in $X$ is topological iff $X$ is strongly…

We consider pairs of maps $(f,g)$, where $f$ is an $n$-valued map and $g$ is an $m$-valued map, defined on connected finite polyhedra. A point $x$ such that $f(x)\cap g(x)\neq \emptyset$ is called a coincidence point of $f$ and $g$. A…

In this paper, we explore a taxonomy of connectivity for space-like structures. It is inspired by isolating posets of connected pieces of a space and examining its embedding in the ambient space. The taxonomy includes in its scope all…

Distributive subsets of the group of all invertible continuous binary operations on a topological space are considered, and it is proved that the subgroups generated by them are also distributive. A criterion for the distributivity of a…

The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…

We investigate a question posed by Huaipeng Chen: if $X$ and $Y$ are paracompact submetrizable spaces and $f:X\to Y$ is a perfect map, can $X$ and $Y$ be submetrized by metrics $\rho$ and $d$ respectively such that $f$ remains perfect with…

For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and $Y$, Uspenskij \cite{us} proved that if…

We characterise the frame morphisms $f:L\to M$ that lift to frame maps $\overline{f}:\mathsf{S}_b(L)\to \mathsf{S}_b(M)$, where $\mathsf{S}_b(L)$ is the collection of joins of complemented sublocales of a frame $L$, or equivalently the…

We consider capacity (fuzzy measure, non-additive probability) on a compactum as a monotone cooperative normed game. We introduce topological analogues of well known class of exact games and show that these classes form subfunctors of the…

In 1967 Hajnal and Juh{\'a}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most $\mathfrak{c}$, the cardinality of the real line. We give an improvement of this…

Metric-preserving functions (here, metric aggregation functions) offer a natural method for constructing metrics on Cartesian products of metric spaces or for aggregating multiple metrics defined on a common set. Strongly metric-preserving…

For any Tychonoff space $X$ let $D(X)$ be either the set $C(X)$ of all continuous functions on $X$ or the set $C^*(X)$ of all bounded continuous functions on $X$. When $D(X)$ is endowed with the point convergence topology, we write…

We introduce the Limiter, a universal extension of the real numbers and of the limit functional that assigns a canonical limit in an enlarged space to every real sequence. Motivated by generalized summation methods such as Borel summation…

In this study, Devaney's chaos conditions are revisited within the framework of descriptive proximity. The concepts of descriptive transitivity, the density of descriptive periodic objects, and descriptive sensitivity are defined. The most…

Game-theoretic characterizations of selection principles provide a powerful framework for analyzing covering properties through strategic interactions. For a Tychonoff space $X$ and a non-trivial metrizable arc-connected topological group…

This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…

In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of…

We study the topology of circularly ordered sets. While the algebraic notion is classical, the general topological theory has received comparatively little attention. In this work we provide a self-contained topological exposition and…