Geodesic
Reflexive families of closed sets
Zhongqiang Yang 1   ; Dongsheng Zhao 2
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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
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

Zhongqiang Yang  1   ; Dongsheng Zhao  2

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 
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Zhongqiang Yang; Dongsheng Zhao. Reflexive families of closed sets. Fundamenta Mathematicae, Tome 192 (2006) no. 2, pp. 111-120. doi: 10.4064/fm192-2-2

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