Corollary 1

Tag 0BWW, permanent. Cite it as [Bourbaki, Tag 0BWW].

General Topology, chapter VI, § 2. Euclidean distance, balls and spheres

The sphere $S_{n-1}$ is homeomorphic to the quotient of $\mathbf{R}_n^*$ by the equivalence relation whose classes are the open rays with origin $o$ .

These classes can also be defined as the classes of intransitivity, other than $\{ o \}$ , of the group of homotheties of ratio $> 0$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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