Lebesgue's number lemma
id:
lebesgue-s-number-lemma-173-2342554
title:
Lebesgue's number lemma
text:
In topology, the Lebesgue covering lemma is a useful tool in the study of compact metric spaces. Given an open cover of a compact metric space, a Lebesgue's number of the cover is a number δ > 0 such that every subset of X having diameter less than δ is contained in some member of the cover. The existence of Lebesgue's numbers for compact metric spaces is given by the Lebesgue's covering lemma:
- If the metric space is compact and an open cover of X is given, then the cover admits some Lebesgu
brand slug:
wiki
category slug:
encyclopedia
description:
Given a cover of a compact metric space, all small subsets are subset of some cover set
original url:
https://en.wikipedia.org/wiki/Lebesgue%27s_number_lemma
date created:
2004-07-15T11:22:11Z
date modified:
2024-09-02T01:11:17Z
main entity:
{"identifier":"Q1049869","url":"https://www.wikidata.org/entity/Q1049869"}
image:
fields total:
13
integrity:
15