Relativization of set strongly star-Menger property

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-07-15 DOI:10.1016/j.topol.2025.109523

Sumit Singh , Anuj Sharma

引用次数: 0

Abstract

A subspace Y of a topological space X is said to have set relatively strongly star-Menger property in X (in short, set-RSSM) if for each nonempty subset M ⊆Y and for each sequence

(U_{n} : n

\in N)

of collections of open sets in X such that

\overline{M} \subseteq ⋃ U_{n}

, for each

n \in N

, there is a sequence

(F_{n} : n

\in N)

of finite subsets of

\overline{M}

such that

M \subseteq ⋃_{n \in N} St (F_{n}

U_{n})

. In this paper, we study the topological properties of set-RSSM subspace and their relationships with various existing related properties.

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集强星-门格尔性质的相对性

假定拓扑空间X的子空间Y在X中具有相对强的星门格尔性质（简称集rssm），如果对于每个非空子集M，并且对于X中的每个开集集合序列（Un:n∈n），使得M⊥∈Un，对于每个n∈n，存在M的有限子集序列（Fn:n∈n），使得M⊥∈NSt（Fn, Un）。本文研究了集合- rssm子空间的拓扑性质及其与现有各种相关性质的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.