Corollary

Tag 01S6, permanent. Cite it as [Bourbaki, Tag 01S6].

Topologie algébrique, chapter I, § 6. Espaces simplement connexes

Every interval of the real line $\mathbf{R}$ is simply connected.

In fact, the connected subspaces of $\mathbf{R}$ are the intervals (TG, IV, p. 8, th. 4) and the intersection of two intervals is an interval.

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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