Proposition 9

Tag 0B6L, permanent. Cite it as [Bourbaki, Tag 0B6L].

General Topology, chapter I, § 8. Hausdorff spaces and regular spaces

If $f$ is a continuous mapping of a topological space $X$ into a Hausdorff space $X'$ , and $R$ is the equivalence relation $f(x) = f(y)$ , then the quotient space $X/R$ is Hausdorff.

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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