Corollary 2

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

The space $\mathbf{R}_n^*$ is homeomorphic to $\mathbf{R} \times S_{n-1}$ .

For $\mathbf{R}_+^* = ]0, +\infty[$ is homeomorphic to $\mathbf{R}$ (Chapter IV, § 4, no. 1, Proposition 1).

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

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Nothing.