Generalizations of chainability and compactness, and the hypertopologies

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2026-01-01 Epub Date: 2025-10-10 DOI:10.1016/j.topol.2025.109635

Ajit Kumar Gupta , Saikat Mukherjee

引用次数: 0

Abstract

We define two properties for subsets of a metric space. One of them is a generalization of chainability, finite chainability, and Menger convexity for metric spaces; and the other extends the notion of compactness for subsets of a metric space. We establish several fundamental results concerning these two properties. Further, in the context of these properties, we study the Hausdorff metric and derive the relations among Hausdorff, Vietoris, and locally finite hypertopologies on the collection of nonempty closed subsets of a metric space.

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链性和紧性的推广，以及超拓扑

我们定义了度量空间子集的两个性质。其中之一是对度量空间的链性、有限链性和门格尔凸性的推广；另一个扩展了度量空间子集的紧性概念。我们建立了关于这两个性质的几个基本结果。进一步，在这些性质的背景下，我们研究了Hausdorff度量，并推导了度量空间的非空闭子集集合上的Hausdorff、Vietoris和局部有限超拓扑之间的关系。

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.