Lebesgue's Number Lemma
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Theorem
Sequentially Compact Space
Let $M = \struct {A, d}$ be a metric space.
Let $M$ be sequentially compact.
Then there exists a Lebesgue number for every open cover of $M$.
Compact Space
Let $M = \struct {X, d}$ be a metric space.
Let $M$ be compact.
Then there exists a Lebesgue number for every open cover of $M$.
Source of Name
This entry was named for Henri Léon Lebesgue.