Remarks on cs-starcompact spaces
Commun. Korean Math. Soc. 2012 Vol. 27, No. 1, 201-205
Printed March 1, 2012
Yan-Kui Song
Nanjing Normal University
Abstract : A space $X$ is $cs$-$starcompact$ if for every open cover $\mathcal U$ of $X$, there exists a convergent sequence $S$ of $X$ such that $St(S,\mathcal U)=X$, where $St(S,{\mathcal U})=\bigcup\{U\in{\mathcal U}: U\cap S\neq\emptyset\}$. In this paper, we prove the following statements: (1) There exists a Tychonoff cs-starcompact space having a regular-closed subset which is not cs-starcompact; (2) There exists a Hausdorff cs-starcompact space with arbitrary large extent; (3) Every Hausdorff centered-Lindel{\"o}f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.
Keywords : compact, countably compact, cs-starcompact
MSC numbers : 54D20, 54G20
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