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 X {\displaystyle X} , a Lebesgue's number of the cover is a number δ > 0 {\displaystyle \delta >0} such that every subset of X {\displaystyle X} having diameter less than δ {\displaystyle \delta } is contained in some member of the cover.
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 X {\displaystyle X} , a Lebesgue's number of the cover is a number δ > 0 {\displaystyle \delta >0} such that every subset of X {\displaystyle X} having diameter less than δ {\displaystyle \delta } is contained in some member of the cover.
Source: Wikipedia "Lebesgue's number lemma" · CC BY-SA 4.0
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