Definition 2

Tag 0B1B, permanent. Cite it as [Bourbaki, Tag 0B1B].

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

A subset $L$ of a topological space $X$ is said to be locally closed at a point $x \in L$ if there is a neighbourhood $V$ of $x$ in $X$ such that $L \cap V$ is a closed subset of the subspace $V$ . L is said to be locally closed in $X$ if it is locally closed at each $x \in L$ .

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

Cited by

Proposition 4, § 2

Cites

Nothing.