Lebesgue number lemma

Lebesgue number lemma: For every open cover 𝒰 of a compactPlanetmathPlanetmath metric space X, there exists a real number δ>0 such that every open ball in X of radius δ is contained in some element of 𝒰.

Any number δ satisfying the property above is called a Lebesgue number for the covering 𝒰 in X.

Title Lebesgue number lemma
Canonical name LebesgueNumberLemma
Date of creation 2013-03-22 13:01:05
Last modified on 2013-03-22 13:01:05
Owner djao (24)
Last modified by djao (24)
Numerical id 5
Author djao (24)
Entry type Theorem
Classification msc 54E45
Defines Lebesgue number