Visual proof that the connected sum of a real projective plane ( represented here as a Moebius strip, but remember that glueing a disc to the border of a Moebius strip produces a real projective plane) and a torus , and the connected sum of a real projective plane and a Klein bottle ar...
- the connected sum of two real projective planes is a Klein bottle: . - the connected sum of three real projective planes (thus of a Klein bottle and a projective plane) is topologically equivalent to the sum of a torus and a real projective plane: ; we get Dyck's surface.The...
Klein bottle, topological space, named for the German mathematician Felix Klein, obtained by identifying two ends of a cylindrical surface in the direction opposite that is necessary to obtain a torus. The surface is not constructible in three-dimensiona