Strong uniform and strong Whitney convergences on C(X,Y)

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-07-17 DOI:10.1016/j.topol.2025.109526

Tarun Kumar Chauhan

引用次数: 0

Abstract

For any two metric spaces

(X, d)

(Y, ρ)

and a bornology

B

on X, we investigate particular subsets of

C (X, Y)

which are clopen under the topology

τ_{B}^{s w}

of strong Whitney convergence on bornology and the topology

τ_{B}^{s}

of strong uniform convergence on bornology. We show that the space

C (X, Y)

endowed with these topologies is not generally connected. In the process, we also provide new characterizations for the notions of shields and bornology that are shielded from closed sets, using these particular subsets of

C (X, Y)

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C（X，Y）上的强一致收敛和强Whitney收敛

对于任意两个度量空间（X,d），（Y,ρ）和X上的一个bornology B，我们研究了C（X，Y）在bornology上强Whitney收敛的拓扑τBsw和bornology上强一致收敛的拓扑τB下闭合的特定子集。我们证明了具有这些拓扑的空间C（X，Y）是不一般连通的。在此过程中，我们还利用C（X，Y）的这些特定子集，为屏蔽和屏蔽于闭集的本体概念提供了新的表征。

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.