Lindelöf's lemma [SEP] named after
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.
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.
Generalized Statement.
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
- Lindelöf's lemma ("topology")
- Lindenbaum's lemma ("mathematical logic")
- Lions's lemma
- Little's lemma ("queuing theory")
- Littlewood–Offord lemma ("combinatorics")
- Łojasiewicz factorization lemma
- Lovász local lemma ("probability theory")
- Margulis lemma ("hyperbolic geometry")
- Matrix determinant lemma ("matrix theory")
- Matrix inversion lemma
- Mautner's lemma ("representation theory"