[:homeomorphism:] [:homeomorphic:] • For a function ff between two topological spaces, if ff is bijective and both ff and f1f^{-1} are continuous, then we say ff is a homeomorphism • Intuition: for f:XYf : X \to Y, continuity of ff means "ff may not tear". Continuity of f1f^{-1} means "ff may not glue" • Equivalent to saying: f(U)f(U) is open iff UU is open • Since ff is a bijection, this means that ff is also giving us a bijection between open sets • Thus, • "The goal of topology is to classify topological spaces up to homeomorphism" • I.e., the set of spaces modulo being homeomorphic Referenced by: