Yan-kui Song
A note on spaces with countable extent

Comment.Math.Univ.Carolin. 58,3 (2017) 397-399.

Abstract:Let $P$ be a topological property. A space $X$ is said to be {\it star P\/} if whenever $\mathcal U$ is an open cover of $X$, there exists a subspace $A\subseteq X$ with property $P$ such that $X=St(A,\mathcal U)$. In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindel\"of, which gives a negative answer to a question of Rojas-S\'anchez and Tamariz-Mascar\'ua.

Keywords: star properties; star Lindel\"of; space with star countable extent

DOI: DOI 10.14712/1213-7243.2015.211
AMS Subject Classification: 54D20 54C10 54B10 54B05