Corollary 2
Tag 0B8E, permanent. Cite it as [Bourbaki, Tag 0B8E].
General Topology, chapter I, § 9. Compact spaces and locally compact spaces
Every continuous mapping of a quasi-compact space into a Hausdorff space is closed. If also is bijective, then is a homeomorphism.
This follows immediately from Corollary 1 and Proposition 4 of no. 3.
In particular:
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
- § 10. Galois extensions
- Corollary 4, § 10
- Corollary 2, § 10
- Proposition 8, § 10
- Proposition 13, § 9
- Proposition 8, § 9
- Corollary 4, § 9
- Definition 1, § 4
- Theorem 1, § 3