Bourbaki

Remark

Tag 023K, permanent. Cite it as [Bourbaki, Tag 023K].

Topologie algébrique, chapter IV, § 5. Théorème de van Kampen

If X is unlaceable, so is Y (IV, p. 349, prop. 8). Since a connected unlaceable space is simply connected by arcs if and only if it is simply connected (IV, p. 344, corollary 1 of Theorem 1), one thus recovers prop. 11 of I, p. 137.

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

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Cites

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Machine translation of the English, by gpt-5-6-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.