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november 2019 A note on monotonically star $\sigma$-compact spaces
Yan-Kui Song, Wei-Feng Xuan
Bull. Belg. Math. Soc. Simon Stevin 26(4): 527-534 (november 2019). DOI: 10.36045/bbms/1576206355

Abstract

A space $X$ is {\it monotonically star $\sigma$-compact} if one assigns to each open cover $\mathcal U$ of $X$ a subspace $s(\mathcal U)\subseteq X$, called a kernel, such that $s(\mathcal U)$ is a $\sigma$-compact subset of $X$, and $st(s(\mathcal U),\mathcal U)=X$, and if $\mathcal V$ refines $\mathcal U$ then $s(\mathcal U)\subseteq s(\mathcal V)$, where $st(s(\mathcal U),\mathcal U)=\bigcup\{U\in \mathcal U:U\cap s(\mathcal U)\neq\emptyset\}.$ In this paper, we investigate the relationship between monotonically star $\sigma$-compact spaces and related spaces, and also study topological properties of monotonically star $\sigma$-compact spaces.

Citation

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Yan-Kui Song. Wei-Feng Xuan. "A note on monotonically star $\sigma$-compact spaces." Bull. Belg. Math. Soc. Simon Stevin 26 (4) 527 - 534, november 2019. https://doi.org/10.36045/bbms/1576206355

Information

Published: november 2019
First available in Project Euclid: 13 December 2019

zbMATH: 07167742
MathSciNet: MR4042399
Digital Object Identifier: 10.36045/bbms/1576206355

Subjects:
Primary: 54D20 , 54D30 , 54D40

Keywords: monotonically star $\sigma$-compact , monotonically star countable , monotonically star Lindelöf , star Lindelöf

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 4 • november 2019
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