On reflexive closed set lattices

Commentationes mathematicae Universitatis Carolinae

Zhongqiang Yang¹ 

关键词: reflexive families of closed sets;    closed set lattice;    hyperspace;    lower semicontinuous set-valued map;   

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 】

For a topological space $X$, let $S(X)$ denote the set of all closed subsets in $X$, and let $C(X)$ denote the set of all continuous maps $fX\to X$. A family $\mathcal A\subseteq S(X)$ is called {\it reflexive\/} if there exists ${\mathcal C}\subseteq C(X)$ such that $\mathcal A = \{A\in S(X)f(A)\subseteq A$ for every $f\in {\mathcal C}\}$. Every reflexive family of closed sets in space $X$ forms a sub complete lattice of the lattice of all closed sets in $X$. In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families of closed sets to be reflexive are obtained.

【 授权许可】

CC BY