Corollary

Tag 0ED6, permanent. Cite it as [Bourbaki, Tag 0ED6].

General Topology, chapter IX, Appendix 1. Espaces de Lindelöf

Every sub-Lindelöf space, and in particular every Polish or Lusin space, is a Lindelöf space.

This follows immediately from the preceding prop. 1 and from the definition of sub-Lindelöf spaces (IX, p. 59, def. 2), since a Polish space admits a countable base.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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