Some properties defined by relative versions of star-covering properties II

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2023-10-02 DOI:10.4995/agt.2023.17926

Maddalena Bonanzinga, Davide Giacopello, Fortunato Maesano

引用次数: 2

Abstract

In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using [2], we "easily" prove that the set strong star Menger and set strong star Hurewicz properties are between countable compactness and the property of having countable extent. Also we show that the extent of a regular set star Menger or a set star Hurewicz space cannot exceed c. Moreover, we construct (1) a consistent example of a set star Menger (set star Hurewicz) space which is not set strongly star Menger (set strongly star Hurewicz) and show that (2) the product of a set star Menger (set star Hurewicz) space with a compact space need not be set star Menger (set star Hurewicz). In particular, (1) and (2) answer some questions posed by Kočinac, Konca and Singh in [17] and [23].

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由恒星覆盖性质的相对版本定义的一些性质II

本文考虑了Menger性质的一些最新的相对版本，即集合强星Menger和集合星Menger性质以及相应的hurewicz型性质。特别地，利用[2]，我们“轻松地”证明了集合强星Menger和集合强星Hurewicz性质介于可数紧性和具有可数范围的性质之间。此外，我们构造了(1)非集强星门格(集强星Hurewicz)的集星门格(集星Hurewicz)空间的一致例子，并证明了(2)集星门格(集星Hurewicz)空间与紧化空间的乘积不必是集星门格(集星Hurewicz)。特别是，(1)和(2)回答了ko inac、Konca和Singh在[17]和[23]中提出的一些问题。

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

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.