Corollary
Tag 0BHW, permanent. Cite it as [Bourbaki, Tag 0BHW].
General Topology, chapter III, § 2. Subgroups, quotient groups, homomorphisms homogeneous spaces, product groups
A subgroup of a topological group is open if and only if it has an interior point. Every open subgroup is closed.
If a subgroup has an interior point, then by translation all the points of are interior and so is open. The second assertion of the corollary is a particular case of Proposition 4.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
- § 2. General results on filtered rings and modules
- Exercise 1, § 2
- Proposition 9, § 2
- Proposition 13, § 4
- Corollary 2, § 7
- Corollary, § 1
- Corollary 2, § 2