Corollary 2

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

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

Let B be a connected topological space locally connected by paths. If, for a point $b$ of B, the group $\pi_1(B, b)$ is reduced to the identity element, the space B is simply connected.

In fact, it follows from corollary 1 that, under these hypotheses, every covering of B is trivializable.

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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