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.

[edit] Statement of the lemma

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

[edit] Alternate version

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

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