Definition 1

Tag 0ED4, permanent. Cite it as [Bourbaki, Tag 0ED4].

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

One says that a topological space $X$ (not necessarily separated) is a Lindelöf space if, from every open covering of $X$ , one can extract a countable covering of $X$ .

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

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