An invertible function f between topological spaces such that f and f^{-1} are both continuous. Topology does not really distinguish between homeomorphic spaces. A sphere and the surface of a cube are homeomorphic; so -- as the cliche example goes -- are the surfaces of a donut and a mug.

Ho`me*o*mor"phism (?), n. [See Homeomorphous.]

A near similarity of crystalline forms between unlike chemical compounds. See Isomorphism.

© Webster 1913.

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