Corollary

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

General Topology, chapter VI, § 3. Real projective spaces

Every point of $\mathbf{P}_n$ has an open neighbourhood homeomorphic to $\mathbf{R}^n$ .

It follows in particular that the real projective spaces are locally connected (this follows also from Chapter I, § II, no. 6, Proposition 12).

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

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