Real projective space

In mathematics, real projective space, denoted ⁠$\mathbb {RP} ^{n}$⁠ or ⁠$\mathbb {P} _{n}(\mathbb {R} ),$⁠ is the topological space of lines passing through the origin 0 in the real space ⁠$\mathbb {R} ^{n+1}.$⁠ It is a compact, smooth manifold of dimension n, and is a special case ⁠$\mathbf {Gr} (1,\mathbb {R} ^{n+1})$⁠ of a Grassmannian space.