Yan-Kui Song, Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210046, P. R. China, e-mail: songyankui@ njnu.edu.cn
Abstract: 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 $X=\mathop St(A,\mathcal U)$, where $\mathop St(A,\mathcal U)=\bigcup\{U\in\mathcal U U\cap A\neq\emptyset\}.$ In this paper, we study the relationships of star $P$ properties for $P\in\{$Lindelof, compact, countably compact$\}$ in pseudocompact spaces by giving some examples.
Keywords: Lindelof, star Lindelof, compact, star compact, countably compact, star countably compact space
Classification (MSC 2010): 54D20, 54A25
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