Related papers: Meekly SC*-Normal Spaces in Topological Spaces

Molodstov[10] introduced soft set theory as a new mathematical approach for solving problems having uncertainties. Many researchers worked on the findings of structures of soft set theory and applied to many problems having uncertainties.…

We will introduce a notion of normal subshifts. A subshift $(\Lambda,\sigma)$ is said to be normal if it satisfies a certain synchronizing property called $\lambda$-synchronizing and is infinite as a set. We have lots of purely infinite…

Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…

The paper introduces the class of O-metric spaces, a novel generalization of metric-type spaces, classifying almost all possible metric types into upward and downward O-metrics. We list some topologies arising from O-metrics and discuss…

The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…

While there is only one natural dimension concept for separable, metric spaces, the theory of dimension in noncommutative topology ramifies into different important concepts. To accommodate this, we introduce the abstract notion of a…

Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of $T_0$ spaces instead of restricting to posets. In this paper, we respond to this calling…

We introduced and study a family of generalized norm on $C^*$-algebras and the notion of Birkhoff-James orthogonality and norm-parallelism with respect to these family of generalized norms are investigated.

The aim of this note is to prove that the set of proper normal subgroups of a group endowed with coarse lower topology is a spectral space.

For any topological space there is a sheaf cohomology. A Grothendieck topology is a generalization of the classical topology such that it also possesses a sheaf cohomology. On the other hand any noncommutative $C^*$-algebra is a…

We 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…

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 propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…

We compare three notions of genericity of separable metric structures. Our analysis provides a general model theoretic technique of showing that structures are generic in descriptive set theoretic (topological) sense and in measure…

In this paper, we continue studying the properties of $\gamma^{*}$-semi-open sets in topological spaces introduced by S. Hussain, B. Ahmad and T. Noiri[8]. We also introduce and discuss the $\gamma^{*}$-semi-continuous functions which…

In this paper, we build up a scaled homology theory, $lc$-homology, for metric spaces such that every metric space can be visually regarded as "locally contractible" with this newly-built homology. We check that $lc$-homology satisfies all…

We define and study the properties of $\gamma^{*}$-regular and $\gamma$-normal spaces. We also continue studying $\gamma_{o}$-compact spaces defined in [5].

We introduce an alternative description of coarse proximities. We define a coarse normality condition for connected coarse spaces and show that this definition agrees with large scale normality defined in [3] and asymptotic normality…

Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…

We introduce a new topological property called (*) and the corresponding class of topological spaces, which includes spaces with $G_\delta$-diagonals and Gruenhage spaces. Using (*), we characterise those Banach spaces which admit…