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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-2-2,
author = {Zhongqiang Yang and Dongsheng Zhao},
title = {Reflexive families of closed sets},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {111-120},
zbl = {1111.47007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-2-2}
}
Zhongqiang Yang; Dongsheng Zhao. Reflexive families of closed sets. Fundamenta Mathematicae, Tome 189 (2006) pp. 111-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-2-2/