Category:Lebesgue's Number Lemma

This category contains pages concerning Lebesgue's Number Lemma:

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.