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Real projective space

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

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