Countable tightness is not discretely reflexive in \(\sigma\)-compact spaces

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2025-03-28 DOI:10.1007/s10474-025-01521-7

I. Juhász, J. van Mill

引用次数: 0

Abstract

Answering a question raised by V.V. Tkachuk in [10], we present several examples of \(\sigma\)-compact spaces, some only consistent and some in ZFC, that are not countably tight but in which the closure of any discrete subset is countably tight. In fact, in some of our examples the closures of all discrete subsets are even first countable.

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可数紧性在\(\sigma\) -紧空间中不是离散自反的

为了回答V.V. Tkachuk在[10]中提出的一个问题，我们给出了几个\(\sigma\) -紧空间的例子，其中一些在ZFC中是一致的，一些在ZFC中是不可数紧的，但其中任意离散子集的闭包是可数紧的。事实上，在我们的一些例子中，所有离散子集的闭包甚至是首可数的。

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

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.