Related papers: Some Separation Axioms in Topological Spaces

Here we have investigated some aspects of $s\lambda$-closed sets on separation axioms including $s T_{2\frac{1}{2}} $ and $s T_{3\frac{1}{2}} $ axioms and on compactness in generalized topological spaces

There are a number of localic separation axioms which are roughly analogous to the $T_1$-axiom from classical topology. For instance, besides the well-known subfitness and fitness, there are also Rosicky-Smarda's $T_1$-locales, totally…

We present a construction of the soft $T_{0}$ reflection of a soft topological space and characterize some separation axioms developed through the soft $T_{0}$ reflection.

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…

This note is an introductory survey of non-Hausdorff separation axioms. The main focus is to study properties that are between $T_0$ and $T_1$, properties between $T_1$ and Hausdorff and how the $T_0$-quotient change them and the relation…

In this paper, we introduce a new method for compactification of a topological space by order topology and through ordinal numbers. The idea behind our approach originates from the definition of a limit point, and then we try to find an…

We introduce soft bitopological spaces from the standpoint of soft elements. A soft bitopological space is a soft set equipped with two soft topologies. Following the classical construction of Goldar--Ray, each soft topology on $F$ induces…

Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, lead to all the others without further recourse to topology.…

An ideal is a nonempty collection of subsets closed under heredity and finite additivity. The aim of this paper is to unify some weak separation properties via topological ideals. We concentrate our attention on the separation axioms…

Recently, Xu proposed a strongly well-filtered space in [24] and systematically investigated some of its properties and characterizations. In this paper, we introduce a new class of T0-spaces called S*-well-filtered spaces, which is…

An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of…

In this paper we study the reflections of the category of topological and semitopological semigroups on the category of the class of topological spaces satisfying separation axioms $T_{0}$, $T_{1}$, $T_{2}$, $T_{3}$ and regular and we apply…

We present the set of axioms for topological space with the operation of boundary as primitive notion.

We systematically study some basic properties of the theory of pre-topological spaces, such as, pre-base, subspace, axioms of separation, connectedness, etc. Pre-topology is also known as knowledge space in the theory of knowledge…

This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A…

Let $\kappa$ be an infinite regular cardinal. We define a topological space $X$ to be $T_{\kappa-Borel}$-space (resp. a $T_{\kappa-BP}$-space) if for every $x\in X$ the singleton $\{x\}$ belongs to the smallest $\kappa$-additive algebra of…

In this paper, we develop new optional stopping theorems for scenarios where the stopping rules are defined by bounded continuity regions. Moreover, we establish a wide variety of inequalities on the supremums and infimums of functions of…

There are several ideal boundaries and completions in General Relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator $L$. As emphasized in a…

The paper develops a novel analysis of mutual interactions between topology and soft topology. It is known that each soft topology produces a system of crisp (parameterized) topologies. The other way round is also possible. Namely, one can…