Mesocompactness and selection theory

Commentationes mathematicae Universitatis Carolinae

Peng-Fei Yan¹ 

关键词: selections;    l.s.c.\ set-valued maps;    mesocompact;    sequentially mesocompact;    persevering compact set-valued maps;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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.

【 授权许可】

CC BY