Definition 1
Tag 0BXI, permanent. Cite it as [Bourbaki, Tag 0BXI].
General Topology, chapter VI, § 3. Real projective spaces
The projective space P_n(R) endowed with the quotient topology of the topology of R_{n+1}^* by the equivalence relation Δ_n(R) is called real projective space of n dimensions.
The projective space P_1(R) is called the real projective line, and P_2(R) is called the real projective plane.
Whenever there is no risk of confusion, we shall write P_n and Δ_n instead of P_n(R) and Δ_n(R).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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