Corollary 1

Tag 0B1O, permanent. Cite it as [Bourbaki, Tag 0B1O].

General Topology, chapter I, § 3. Subspaces, quotient spaces

If A is an open (resp. closed) subset of X which is saturated with respect to R, then the canonical mapping $h : A/R_A \to f(A)$ is a homeomorphism.

For if A is open (resp. closed) in X and saturated with respect to R, and if $B \subset A$ is open (resp. closed) in A and saturated with respect to $R_A$ , then B is open (resp. closed) in X and saturated with respect to R.

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

Cited by

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Cites

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