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Reflexive families of closed sets

Tom 192 / 2006

Fundamenta Mathematicae 192 (2006), 111-120 MSC: 47A15, 54C05, 54D05, 54E45. DOI: 10.4064/fm192-2-2

Streszczenie

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.

Autorzy

• Zhongqiang YangDepartment of Mathematics
Shantou University
Shantou, Guangdong, 515063, P.R. China
e-mail
• Dongsheng ZhaoMathematics and Mathematics Education
National Institute of Education
Nanyang Technological University
1 Nanyang Walk, Singapore 637616
e-mail

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