Induced mappings on Pixley-Roy hyperspace

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-10 DOI:10.1016/j.topol.2025.109389

Enrique Castañeda-Alvarado, David Maya, Miguel Angel Morales-Bautista, Fernando Orozco-Zitli

引用次数: 0

Abstract

The symbol

PR [X]

denotes the hyperspace consisting of all nonempty finite subsets of a

T_{1}

topological space X endowed with the Pixley-Roy topology. For an onto mapping between

T_{1}

spaces

f : X \to Y

, define the induced mapping

PR (f) : PR [X] \to PR [Y]

PR (f) (A) = {f (a) : a \in A}

(the image of A under f). In this paper, we study the relationship between the condition f belongs to a class of mappings between

T_{1}

spaces

M

and the condition

PR (f)

belongs to

M

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Pixley-Roy超空间上的诱导映射

符号PR[X]表示由具有Pixley-Roy拓扑的T1拓扑空间X的所有非空有限子集组成的超空间。对于T1空间f:X→Y之间的映入映射，通过PR(f)(A)={f(A): A∈A} （A在f下的像）定义了PR(f):PR[X]→PR[Y]的诱导映射PR(f):PR[X]。本文研究了条件f属于T1空间M之间的一类映射与条件PR(f)属于M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.