On \(\mathcal K\)-starcompact spaces. (English) Zbl 1134.54314

Song, Yan-Kui

Bull. Malays. Math. Sci. Soc. (2) 30, No. 1, 59-64 (2007).

Summary: A space \(X\) is \(\mathcal K\)-starcompact if for every open cover \(\mathcal U\) of \(X\), there exists a compact subset \(K\) of \(X\) such that \(St(K,{\mathcal U})=X\), where \(St(K,{\mathcal U})=\bigcup\{U\in{\mathcal U}: U\cap K\neq\emptyset\}\). In this paper, we investigate the relations between \(\mathcal K\)-starcompact spaces and other related spaces. We also study topological properties of \(\mathcal K\)-starcompact spaces.

MSC:

54D20	Noncompact covering properties (paracompact, Lindelöf, etc.)
54B10	Product spaces in general topology
54D55	Sequential spaces

Keywords:

countably compact; star-compact; \(1\frac12\)-star compact