Remark 2

Tag 0B0A, permanent. Cite it as [Bourbaki, Tag 0B0A].

General Topology, chapter I, § 2. Continuous functions

To verify that a continuous bijection $f : X \to X'$ is a homeomorphism, it is enough to show that for each $x \in X$ and each neighbourhood $V$ of $x$ , $f(V)$ is a neighbourhood of $f(x)$ in $X'$ .

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

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