Remark 1

Tag 0B09, permanent. Cite it as [Bourbaki, Tag 0B09].

General Topology, chapter I, § 2. Continuous functions

It is possible to have a continuous bijection of a topological space $X$ onto a topological space $X'$ which is not bicontinuous: for example, take $X'$ to be the rational line $\mathbf{Q}$ , and $X$ to be the set $\mathbf{Q}$ with the discrete topology; then the identity map $X \to X'$ is continuous but is not a homeomorphism.

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

Cited by

Remark, § 2

Cites

Nothing.