Reflexive families of closed sets
Volume 192 / 2006
Fundamenta Mathematicae 192 (2006), 111-120
MSC: 47A15, 54C05, 54D05, 54E45.
DOI: 10.4064/fm192-2-2
Abstract
Let $S(X)$ denote the set of all closed subsets of a topological space $X$, and $C(X)$ the set of all continuous mappings $f:X\to X$. A family ${\cal A}\subseteq S(X)$ is called reflexive if there exists ${\mathcal F}\subseteq C(X)$ such that ${\cal A}= \{A\in S(X): f(A)\subseteq A {\rm\ for\ every\ }f\in {\mathcal F}\}$. We investigate conditions ensuring that a family of closed subsets is reflexive.
