Lindelöf's lemma

Lindelöf's lemma

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.

tatement of the lemma

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

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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