homeomorphism Homeomorphism 2001-11-16 18:19:53 2006-10-14 11:23:01 Definition homeomorphic autohomeomorphism auto-homeomorphism self-homeomorphism \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} A \emph{homeomorphism} $f$ of topological spaces is a continuous, bijective map such that $f^{-1}$ is also continuous. We also say that two spaces are \emph{homeomorphic} if such a map exists. If two topological spaces are homeomorphic, they are topologically equivalent --- using the techniques of topology, there is no way of distinguishing one space from the other. An \emph{autohomeomorphism} (also known as a \emph{self-homeomorphism}) is a homeomorphism from a topological space to itself.