A space X is cs-starcompact if for every open cover of X, there exists a convergent sequence S of X such that St(S, ) = X, where . 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-Lindelf space can be embedded in a Hausdorff cs-starcompact space as a closed subspace.
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