Bourbaki

Definition 3

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

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

A topological space X is said to be arcwise connected if for every pair (x,y)(x, y) of points of X, there exists a path of origin xx and of term yy.

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.