Bourbaki

Definition 4

Tag 01X2, permanent. Cite it as [Bourbaki, Tag 01X2].

Topologie algébrique, chapter III, § 2. Homotopie et chemins

A topological space is said to be locally path-connected if each of its points possesses a fundamental system of path-connected neighbourhoods.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.

Machine translation of the English, by gpt-5-6-mini, gpt-5-mini, gpt-5-6, gpt-5.4, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.