On increasing, locally persistent and persistent Whitney properties

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-07-01 DOI:10.1016/j.topol.2025.109492

José Gerardo Ahuatzi-Reyes , Norberto Ordoñez , Hugo Villanueva

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引用次数: 0

Abstract

Let X be a metric continuum and let

C (X)

be the hyperspace of subcontinua of X. The problem of determining which topological properties are Whitney properties has been widely studied and has generated an ample line of research. This line has been enriched with new concepts, such as that of increasing Whitney property, which was studied in [18]. In order to extend these ideas in other directions, in this paper we introduce two new concepts: Whitney persistent property and locally Whitney persistent property (see Definition 1.1). We establish the relations that exist between these concepts and those of Whitney and increasing properties. Also, we determine, from a long list of topological properties, which ones are or are not increasing, locally persistent or persistent. For these purposes, we provided some general results and several examples. Part of this work extends the study given in [18].

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关于递增、局部持久和持久的惠特尼性质

设X为度量连续统，C(X)为X的次连续统的超空间。确定哪些拓扑性质是惠特尼性质的问题已经得到了广泛的研究，并产生了大量的研究方向。这条线被新的概念所丰富，例如b[18]中研究的增加惠特尼性质。为了在其他方向上扩展这些思想，本文引入了两个新概念：Whitney持久化性质和局部Whitney持久化性质（见定义1.1）。我们建立了这些概念与惠特尼和递增性质之间存在的关系。此外，我们还从一长串拓扑属性中确定哪些是递增的，哪些是递增的，哪些是局部持久的，哪些是持久的。出于这些目的，我们提供了一些一般结果和几个示例。这项工作的一部分扩展了b[18]中给出的研究。

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.