Bourbaki

Corollary 1

Tag 01X4, permanent. Cite it as [Bourbaki, Tag 01X4].

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

Every connected open subset of a locally path-connected topological space is path-connected.

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.