Proposition 9

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

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

The Grassmannian $G_{n,p}$ is homeomorphic to the space $P_{n,p}$ .

We recall finally that the Grassmannians $G_{n,p}(K)$ and $G_{n,n-p-1}(K)$ are subsets of the same projective space $P_{n-1}(K)$ and can be transformed into the other by a projective linear transformation; it follows that $G_{n,p}$ and $G_{n,n-p-1}$ are homeomorphic.

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

Cited by

Definition 2, § 4
Exercise 6, § 4

Cites

Nothing.