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Related papers: Separation axioms of $\alpha^{m}$-open sets

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This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…

General Topology · Mathematics 2021-03-09 Xun Ge , Jianhua Gong , Ivan Reilly

In this paper we define the concepts of $g.\Lambda_s$-sets and $g.V_s$-sets and we use them in order to obtain new characterizations of semi-T_1-, semi-R_0- and semi-T_{1/2}-spaces.

General Topology · Mathematics 2007-05-23 Miguel Caldas Cueva , Julian Dontchev

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…

General Mathematics · Mathematics 2014-01-28 E. Peyghan , B. Samadi , A. Tayebi

The separation of two sets (or more specific of two cones) plays an important role in different fields of mathematics such as variational analysis, convex analysis, convex geometry, optimization. In the paper, we derive some new results for…

Functional Analysis · Mathematics 2023-08-04 Christian Günther , Bahareh Khazayel , Christiane Tammer

Generalized topological spaces in the sense of Cs\'{a}sz\'{a}r have two main features which distinguish them from typical topologies. First, these families of subsets are not closed under intersections. Second, we allow for the possibility…

Logic · Mathematics 2019-09-23 Tomasz Witczak

We define a basis property that an inclusion of C*-algebras $\mathcal O_\infty\subset A$ may have, and give various conditions for the property to hold. Some applications are considered. We also give a characterization of open projections…

Operator Algebras · Mathematics 2023-06-28 Dan Kucerovsky

In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…

General Topology · Mathematics 2025-04-08 Abhishikta Das , T. Bag

This survey presents some historical background and recent developments in the area of selections for set-valued mappings along with several open questions. It was written with the hope that the presented material may pique an interest in…

General Topology · Mathematics 2018-10-16 Valentin Gutev

We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.

Discrete Mathematics · Computer Science 2025-07-09 Thierry Marchant , Sandip Sarkar

We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.

General Topology · Mathematics 2016-05-10 Alexander V. Osipov , Selma Özçağ

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.

General Topology · Mathematics 2016-04-18 Alexander V. Osipov

First, we consider some fundamental properties including dual spaces, complex interpolations of $\alpha$-modulation spaces $M^{s,\alpha}_{p,q}$ with $0<p,q \le \infty$. Next, necessary and sufficient conditions for the scaling property and…

Functional Analysis · Mathematics 2012-07-26 Jinsheng Han , Baoxiang Wang

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

General Topology · Mathematics 2020-09-17 Piotr Pikul

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

History and Overview · Mathematics 2013-07-01 Felix Nagel

It is well-known that point-set topology (without additional structure) lacks the capacity to generalize the analytic concepts of completeness, boundedness, and other typically-metric properties. The ability of metric spaces to capture this…

General Topology · Mathematics 2010-11-18 Annie Carter , Daniel Lithio , Robert Niichel , Tristan Tager

Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence…

Rings and Algebras · Mathematics 2024-04-24 Ambroise Grau

The concepts of exterior and boundary in multiset topological space are introduced. We further established few relationships between the concepts of boundary, closure, exterior and interior of an M- set. These concepts have been pigeonholed…

General Mathematics · Mathematics 2015-01-29 J. Mahanta , D. Das

The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…

Functional Analysis · Mathematics 2020-12-15 S. Dutta , S. Singh

Let $A_{1},...A_{m}$ be a $n\times n$ invertible matrices. Let $0 \leq \alpha<n$ and $0<\alpha_{i}<n$ such that $\alpha_1 + ... + \alpha_m = n- \alpha$. We define% \begin{equation*} T_{\alpha}f(x)=\int \frac{1}{\left\vert…

Classical Analysis and ODEs · Mathematics 2024-10-09 Lucas Alejandro Vallejos , Marta Susana Urciuolo

First of all, we focused soft {\beta}-open sets and soft {\beta}-closed sets over the soft topological space and investigated some properties of them. Secondly, we defined the concepts soft {\beta}-continuity, soft {\beta}-irresolute and…

General Topology · Mathematics 2013-12-30 Yunus Yumak , Aynur Keskin Kaymakcı