Definition 3

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

Topologie algébrique, chapter IV, § 1. Espaces délaçables

A topological space B is said to be locally contractible if every point $b$ of B possesses a neighbourhood V such that the pointed space $(V, b)$ is contractible (III, p. 234, example 3).

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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