 Real projective space

Real projective space is the antipodal quotient ${\mathbb{RP}}^n=S^n/(x\sim -x)$.

Real projective space, denoted as \(\mathbb{RP}^n\), is a fundamental concept in topology and geometry. It is defined as the set of lines through the origin in \(\mathbb{R}^{n+1}\).

In those cases at least, it is possible to add a metric to the spaces, leading to elliptic geometry.