Related papers: Topologies of open complemented subsets
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
We define and study a class of finite topological spaces, which model the cell structure of a space obtained by gluing finitely many Euclidean convex polyhedral cells along congruent faces. We call these finite topological spaces,…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
This article begins by deriving a measure-theoretic decomposition of continuous linear functionals on $C(X)$, the space of all real-valued continuous functions on a metric space $(X, d)$, equipped with the topology $\tau_\mathcal{B}$ of…
The Boolean algebra of regular closed sets is prominent in topology, particularly as a dual for the Stone-Cech compactification. This algebra is also central for the theory of geometric computation, as a representation for combinatorial…
In this paper we continue to study the property of separability of functional space C(X) with the open-point and bi-point-open topologies.
The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN…
For a topological space X, let (RX)s := (RX,Ts) be the cartesian product of |X| copies of the real line R with the topology of the uniform convergence on separable subsets of X. In this article we analyze the subspace C(X) of (RX)s of all…
We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…
The concept of Central sets, introduced by Furstenberg through the framework of topological dynamics, has played a pivotal role in combinatorial number theory. Furstenberg's Central Sets Theorem highlighted their rich combinatorial…
Open sets and compact saturated sets enjoy a perfect formal symmetry, at least for classes of spaces such as Stone spaces or spectral spaces. For larger classes of spaces, a perfect symmetry may not be available, although strong signs of it…
The most general definition of a continuous function requires that the preimage of any open set be open. Thus, to discuss continuity in the abstract, it is necessary to first define a topology, which tells us which sets in a space are open.…
We give a characterization of countable discrete subspace $A$ of a topological space $X$ such that there exists a (linear) continuous mapping $\varphi:C_p^*(A)\to C_p(X)$ with $\varphi(y)|_A=y$ for every $y\in C_p^*(A)$. Using this…
Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…
Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…
Building on the recent work of Mushaandja and Olela-Otafudu~\cite{MushaandjaOlela2025} on modular metric topologies, this paper investigates extended structural properties of modular (pseudo)metric spaces. We provide necessary and…
Given a closed orientable surface (\Sigma) of genus at least two, we establish an affine isomorphism between the convex compact set of isotopy-invariant topological measures on (\Sigma) and the convex compact set of additive functions on…
The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski topos. In this paper we apply such techniques to the higher…
We survey different topologizations of the set $\mathcal{S}(G)$ of all closed subgroups of a topological group $G$ and demonstrate some applications in Topological Grous, Model Theory, Geometric Group Theory, Topological Dynamics.
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…