Mapping-cylinder model of punctured real projective three-space
= Mapping-cylinder model of punctured real projective three-space
The complement of an open three-ball in $\mathbb{RP}^3$ is the mapping cylinder of the antipodal covering $S^2\to\mathbb{RP}^2$. It deformation retracts to $\mathbb{RP}^2$ and has boundary $S^2$.