Definition 1

Tag 0B13, permanent. Cite it as [Bourbaki, Tag 0B13].

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

Let $A$ be a subset of a topological space $X$ . The topology induced on $A$ by the topology of $X$ is that in which the open sets are the intersections with $A$ of open sets of $X$ . The set $A$ with this topology is called a subspace of $X$ .

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

Cited by

Example, § 3

Cites

Nothing.