Closure-preserving covers in function spaces

Commentationes mathematicae Universitatis Carolinae

David Guerrero Sánchez¹ 

关键词: closure-preserving covers;    function spaces;    compact spaces;    pointwise convergence topology;    topological game;    winning strategy;   

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 】

It is shown that if $C_p(X)$ admits a closure-preserving cover by closed $\sigma$-compact sets then $X$ is finite. If $X$ is compact and $C_p(X)$ has a closure-preserving cover by separable subspaces then $X$ is metrizable. We also prove that if $C_p(X,[0,1])$ has a closure-preserving cover by compact sets, then $X$ is discrete.

【 授权许可】

CC BY