Reflexive families of closed sets

Zhongqiang Yang, and Dongsheng Zhao. "Reflexive families of closed sets." Fundamenta Mathematicae 192.2 (2006): 111-120. <http://eudml.org/doc/283386>.

@article{ZhongqiangYang2006,
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 → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = \{A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ\}. We investigate conditions ensuring that a family of closed subsets is reflexive.},
author = {Zhongqiang Yang, Dongsheng Zhao},
journal = {Fundamenta Mathematicae},
keywords = {reflexive family of closed sets; s-reflexive topological space; strongly zero-dimensional metric space; hereditarily disconnected space; reflexive closed set},
language = {eng},
number = {2},
pages = {111-120},
title = {Reflexive families of closed sets},
url = {http://eudml.org/doc/283386},
volume = {192},
year = {2006},
}

TY - JOUR
AU - Zhongqiang Yang
AU - Dongsheng Zhao
TI - Reflexive families of closed sets
JO - Fundamenta Mathematicae
PY - 2006
VL - 192
IS - 2
SP - 111
EP - 120
AB - 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 → X. A family 𝓐 ⊆ S(X) is called reflexive if there exists ℱ ⊆ C(X) such that 𝓐 = {A ∈ S(X): f(A) ⊆ A for every f ∈ ℱ}. We investigate conditions ensuring that a family of closed subsets is reflexive.
LA - eng
KW - reflexive family of closed sets; s-reflexive topological space; strongly zero-dimensional metric space; hereditarily disconnected space; reflexive closed set
UR - http://eudml.org/doc/283386
ER -