Bourbaki

Definition 5

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

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

Let X and Y be topological spaces. A mapping f:X→Yf: X\rightarrow Y is said to be arcwise continuous if, for every path cc in X, the mapping f∘c:I→Yf\circ c:\mathbf{I}\rightarrow Y is continuous.

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.