Remarks on SHD spaces and more divergence properties

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-08-30 DOI:10.1016/j.topol.2024.109055

Carlos David Jiménez-Flores , Alejandro Ríos-Herrejón , Alejandro Darío Rojas-Sánchez , Artur Hideyuki Tomita , Elmer Enrique Tovar-Acosta

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Abstract

The class of SHD spaces was recently introduced in [12]. The first part of this paper focuses on answering most of the questions presented in that article. For instance, we exhibit an example of a non-SHD Tychonoff space X such that $F [X]$ , the Pixley-Roy hyperspace of X, βX, the Stone-Čech compactification of X, and $C_{p} (X)$ , the ring of continuous functions over X equipped with the topology of pointwise convergence, are SHD.

In the second part of this work we will present some variations of the SHD notion, namely, the WSHD property and the OHD property. Furthermore, we will pay special attention to the relationships between X and $F [X]$ regarding these new concepts.

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关于 SHD 空间和更多发散特性的评论

最近，[12] 一文介绍了 SHD 空间类。本文的第一部分主要回答该文提出的大部分问题。例如，我们举例说明了一个非 SHD 的 Tychonoff 空间 X，使得 X 的 Pixley-Roy 超空间 F[X]、X 的 Stone-Čech compactification βX 和 X 上的连续函数环 Cp(X) 以及点收敛拓扑都是 SHD。此外，我们还将特别关注关于这些新概念的 X 与 F[X] 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.

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