Lindelöf's lemma

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In mathematics, Lindelöf's lemma is a simple but useful lemma in topology on the real line, named for the Finnish mathematician Ernst Leonard Lindelöf.

Statement of the lemma[edit]

Let the real line have its standard topology. Then every open subset of the real line is a countable union of open intervals.

Generalization[edit]

Lindelöf's lemma is also known as the statement that every open cover in a second-countable space has a countable subcover (Kelley 1955:49) This means that every second-countable space is also a Lindelöf space.

References[edit]

J.L. Kelley (1955), General Topology, van Nostrand.