Corollary 1
Tag 0B90, permanent. Cite it as [Bourbaki, Tag 0B90].
General Topology, chapter I, § 9. Compact spaces and locally compact spaces
*With the notation of Proposition 15, every compact subset of is contained in some .
For can be covered by a finite number of the , by axiom (C''').
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.