1Department of Mathematics Shantou University Shantou, Guangdong, 515063, P.R. China 2Mathematics 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
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.
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
Affiliations des auteurs :
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
@article{10_4064_fm192_2_2,
author = {Zhongqiang Yang and Dongsheng Zhao},
title = {Reflexive families of closed sets},
journal = {Fundamenta Mathematicae},
pages = {111--120},
year = {2006},
volume = {192},
number = {2},
doi = {10.4064/fm192-2-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm192-2-2/}
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TY - JOUR
AU - Zhongqiang Yang
AU - Dongsheng Zhao
TI - Reflexive families of closed sets
JO - Fundamenta Mathematicae
PY - 2006
SP - 111
EP - 120
VL - 192
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4064/fm192-2-2/
DO - 10.4064/fm192-2-2
LA - en
ID - 10_4064_fm192_2_2
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