On the class of topological spaces, a homeomorphism class is an equivalence class under the relation of being homeomorphic. For example, the open interval and the space of real numbers , both with their usual topology, are in the same homeomorphism class, as the map

This entry contributed by Rasmus Hedegaard

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Hedegaard, Rasmus. "Homeomorphism Class." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/HomeomorphismClass.html