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Notes on star covering properties
Quaestiones Mathematicae ( IF 0.6 ) Pub Date : 2020-10-14 , DOI: 10.2989/16073606.2020.1825021
Yan-Kui Song 1 , Wei-Feng Xuan 2
Affiliation  

Abstract

In this paper, we show the following statements:

(1) There exists a pseudocompact star Lindelöf Tychonoff space which is not star σ-compact.

(2) There exists a Tychonoff pseudocompact star countable (hence, star Lindelöf) space having a pseudocompact, Gδ regular closed subspace which is not star Lindelöf.

(3) Assuming , there exists a normal star countable (hence, star Lindelöf) space having a Gδ regular closed subspace which is not star Lindelöf.

(4) Let X be a space, then A(X) is star Lindelöf if and only if e(X) ≤ ω. The statement (1) gives a negative answer to Song [13, Remark 2.3].



中文翻译:

星覆盖特性的注意事项

摘要

在本文中,我们展示了以下陈述:

(1) 存在一个伪致密恒星Lindelöf Tychonoff 空间,它不是恒星σ 致密的。

(2) 存在一个 Tychonoff 赝致密星可数空间(因此,林德洛夫星)空间具有一个赝致密G δ正则闭合子空间,它不是林德洛夫星。

(3) 假设,存在一个正常的可数星(因此,星林德洛夫)空间,其G δ正则闭合子空间不是林德洛夫星。

(4) 设X是一个空间,那么A ( X ) 是 Star Lindelöf 当且仅当e ( X ) ≤ ω。陈述 (1) 对 Song [13, Remark 2.3] 给出了否定的回答。

更新日期:2020-10-14
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