$\RP^2$ is a Möbius band capped off by a disk.Suggest a slogan
The real projective plane is obtained from a Möbius band \(\bbm\) and a closed disc \(D^2\) by identifying the boundary circle of \(\bbm\) with \(\partial D^2\) by a homeomorphism: \[ \RP^2 \cong \bbm \union_{\partial} D^2 .\]
Gluing two Möbius bands along their boundary circles gives the Klein bottle [@Hat02].