Definition:Projective Plane/Real

Definition

The real projective plane $\R P^2$ is the projective plane over the field of real numbers.

That is, it is the topological subspace of the $3$-dimensional real Euclidean space $\R^3$ obtained by removing the origin $\tuple {0, 0, 0}$ and identifying together $\tuple {x, y, z}$ and $\tuple {r x, r y, r z}$ for all $r \in \R_{\ne 0}$.

Also see

• Results about real projective plane can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): projective plane
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): projective plane