Question

What is the boundary of rp^n with antipodal points?

Answer 1

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