Peng-Fei Yan, Zhongqiang Yang
Mesocompactness and selection theory

Comment.Math.Univ.Carolin. 53,1 (2012) 149-157.

Abstract:A topological space $X$ is called {\it mesocompact\/} ({\it sequentially mesocompact\/}) if for every open cover ${\mathcal U}$ of $X$, there exists an open refinement ${\mathcal V}$ of ${\mathcal U}$ such that $\{V\in {\mathcal V}: V\cap K\neq \emptyset\}$ is finite for every compact set (converging sequence including its limit point) $K$ in $X$. In this paper, we give some characterizations of mesocompact (sequentially mesocompact) spaces using selection theory.

Keywords: selections, l.s.c.\ set-valued maps, mesocompact, sequentially mesocompact, persevering compact set-valued maps
AMS Subject Classification: 54C65 54C60