Every diffeomorphism is a homeomorphism, but not every homeomorphism is a diffeomorphism. A bijective local homeomorphism is therefore a homeomorphism. A bijective continuous function with continuous inverse function is called a "homeomorphism". This is an example of a homeomorphism that is not a diffeomorphism. Two spaces are called "homeomorphic" if there exists a homeomorphism between them. The FPP is a topological invariant, i.e. is preserved by any homeomorphism. Topological spaces can be broadly classified, up to homeomorphism, by their topological properties. A self-homeomorphism is a homeomorphism from a topological space onto itself. A bilipschitz mapping is injective, and is in fact a homeomorphism onto its image. Let formula 1 be a topological space, and formula 2 a homeomorphism. Classifications up to homeomorphism and homotopy equivalence are known, as follows. A cofibration "f" is always injective, in fact a homeomorphism to its image. Its equivalence classes are called homeomorphism classes. In general topology, an embedding is a homeomorphism onto its image. The mug serves as one of the most popular examples of homeomorphism in topology.