Reflexive families of closed sets

Zhongqiang Yang¹ ; Dongsheng Zhao²

¹ Department of Mathematics Shantou University Shantou, Guangdong, 515063, P.R. China
² Mathematics and Mathematics Education National Institute of Education Nanyang Technological University 1 Nanyang Walk, Singapore 637616

Fundamenta Mathematicae, Tome 192 (2006) no. 2, pp. 111-120

Résumé

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.

Détail

DOI : 10.4064/fm192-2-2

Keywords: denote set closed subsets topological space set continuous mappings family cal subseteq called reflexive there exists mathcal subseteq cal subseteq every mathcal investigate conditions ensuring family closed subsets reflexive