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On minimal strongly KC-spaces

Weihua Sun; Yuming Xu; Ning Li — 2009

Czechoslovak Mathematical Journal

In this article we introduce the notion of strongly $KC$ -spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space $(X, τ)$ is maximal countably compact if and only if it is minimal strongly $KC$ , and apply this result to study some properties of minimal strongly $KC$ -spaces, some of which are not possessed by minimal $KC$ -spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether every...

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