Proposition 3
Tag 0B84, permanent. Cite it as [Bourbaki, Tag 0B84].
General Topology, chapter I, § 9. Compact spaces and locally compact spaces
Every closed subset of a quasi-compact (resp. compact) space is quasi-compact (resp. compact).
This is an immediate consequence of axiom if we remark that if is closed in then every set which is closed in is closed in .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
- Proposition 8, § 10
- Corollary, § 9
- Proposition 13, § 9
- Proposition 8, § 9
- Corollary 2, § 9
- Theorem 4 (Alexandroff), § 9
Cites
Nothing.