Collectionwise normal space
id:
collectionwise-normal-space-319-6715114
title:
Collectionwise normal space
text:
In mathematics, a topological space X is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X there exists a pairwise disjoint family of open sets Ui (i ∈ I), such that Fi ⊆ Ui. Here a family F of subsets of X is called discrete when every point of X has a neighbourhood that intersects at most one of the sets from F .
An equivalent definition of collectionwise normal demands that the above Ui (i ∈ I) themselves form a discrete family, which is stronger than
brand slug:
wiki
category slug:
encyclopedia
description:
Property of topological spaces stronger than normality
original url:
https://en.wikipedia.org/wiki/Collectionwise_normal_space
date created:
date modified:
2023-09-15T00:20:29Z
main entity:
{"identifier":"Q5146123","url":"https://www.wikidata.org/entity/Q5146123"}
image:
fields total:
13
integrity:
14