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.
Contents
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.
Generalization
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
Lindelöf's lemma Wikipedia(Text) CC BY-SA