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.