Bulletin of the Belgian Mathematical Society - Simon Stevin

Remarks on star-K-Menger spaces

Yan-Kui Song

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Abstract

A space $X$ is {\it star-K-Menger} if for each sequence $(\mathcal U_n:n\in\Bbb N)$ of open covers of $X$ there exists a sequence $(K_n:n\in N)$ of compact subsets of $X$ such that $\{St(K_n,\mathcal U_n):n\in\Bbb N\}$ is an open cover of $X$. In this paper, we construct an example of a Hausdorff star-Menger space that is not star-K-Menger which gives an answer to a question of Song [12], and continue to investigate topological properties of star-K-Menger spaces.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 5 (2015), 697-706.

Dates
First available in Project Euclid: 17 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1450389241

Digital Object Identifier
doi:10.36045/bbms/1450389241

Mathematical Reviews number (MathSciNet)
MR3435075

Zentralblatt MATH identifier
1335.54028

Subjects
Primary: 54D20: Noncompact covering properties (paracompact, Lindelöf, etc.) 54C10: Special maps on topological spaces (open, closed, perfect, etc.)

Keywords
Selection principles star-Menger strongly star-Menger star-K-Menger starcompact star Lindelöf strongly starcompact strongly star Lindelöf star-L-Lindelöf

Citation

Song, Yan-Kui. Remarks on star-K-Menger spaces. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 5, 697--706. doi:10.36045/bbms/1450389241. https://projecteuclid.org/euclid.bbms/1450389241


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