Remark 1

Tag 020A, permanent. Cite it as [Bourbaki, Tag 020A].

Topologie algébrique, chapter IV, § 1. Espaces délaçables

There exist topological spaces B, connected and locally arcwise connected, such that certain points $a$ of B, but not all, possess a neighbourhood V such that the homomorphism of $\pi_1(V, a)$ into $\pi_1(B, a)$ is trivial (III, p. 336, exerc. 6).

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.

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