Algebraic Topology | 2021
Classification Theorem of Compact Surfaces
Abstract
We now take a small diversion to discuss some interesting properties of the projective plane and the Klein bottle that we introduced in the previous chapter. Recall that these are abstract surfaces that exist in their own right, without reference to an embedding space like \\(\\mathbb {R}^3\\), but which nonetheless are locally homeomorphic to open sets in the plane.