Lebesgue number lemma

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

Any number $\delta$ 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