Remark 1

Tag 0200, permanent. Cite it as [Bourbaki, Tag 0200].

Topologie algébrique, chapter III, § 5. Homotopie et revêtements (cas des espaces localement connexes par arcs)

If $B_0$ denotes the path-connected component of $a$ in B, the canonical isomorphism $\pi_1(B_0, a)\rightarrow \pi_1(B, a)$ is an isomorphism of topological groups when these groups are endowed with the admissible topology.

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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Cites

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