Geodesic
Remarks on star covering properties in pseudocompact spaces
Mathematica Bohemica, Tome 138 (2013) no. 2, pp. 165-169

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Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $\mathcal U$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=\mathop {\rm St}(A,\mathcal U)$, where $\mathop {\rm St}(A,\mathcal U)=\bigcup \{U\in \mathcal U\colon U\cap A\neq \emptyset \}.$ In this paper, we study the relationships of star $P$ properties for $P\in \{\textrm{Lindelöf, compact, countably compact}\}$ in pseudocompact spaces by giving some examples.
Let $P$ be a topological property. A space $X$ is said to be star $P$ if whenever $\mathcal U$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=\mathop {\rm St}(A,\mathcal U)$, where $\mathop {\rm St}(A,\mathcal U)=\bigcup \{U\in \mathcal U\colon U\cap A\neq \emptyset \}.$ In this paper, we study the relationships of star $P$ properties for $P\in \{\textrm{Lindelöf, compact, countably compact}\}$ in pseudocompact spaces by giving some examples.
DOI : 10.21136/MB.2013.143288
Classification : 54A25, 54D20
Keywords: Lindelöf; star Lindelöf; compact; star compact; countably compact; star countably compact space 
Song, Yan-Kui. Remarks on star covering properties in pseudocompact spaces. Mathematica Bohemica, Tome 138 (2013) no. 2, pp. 165-169. doi: 10.21136/MB.2013.143288
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