• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.201-205
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• 2012

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 $St(S,\mathcal{U})\;=\; \cup\{U{\in}\mathcal{U}:U{\cap}S{\neq}\phi\}$. 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$\ddot{o}$f space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.