Definition 3
Tag 01RY, permanent. Cite it as [Bourbaki, Tag 01RY].
Topologie algébrique, chapter I, § 6. Espaces simplement connexes
A topological space is said to be simply connected if all its coverings are trivializable.
A simply connected space is connected. In fact, if a space X is the disjoint union of two nonempty open sets U and V, the canonical injection of U into X is a covering which is not trivializable.
The empty space is simply connected. Every topological space reduced to a point is simply connected.
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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