Definition 1

Tag 0BW3, permanent. Cite it as [Bourbaki, Tag 0BW3].

General Topology, chapter VI, § 1. Real number space R^n

The topological product of n spaces identical with the real line is called real number space of n dimensions, and is denoted by $\mathbf{R}^n$ .

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

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