homeomorphism [hoh-mee-uh -mawr -fiz-uh m]

Word Origin

similarity in crystalline form but not necessarily in chemical composition. Mathematics . a function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous. Show More

Related forms ho·me·o·mor·phic , ho·me·o·mor·phous , adjective Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

British Dictionary definitions for homeomorphism homeomorphism homoeomorphism

the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces Show More

Derived Forms homeomorphic , homeomorphous , homoeomorphic or homoeomorphous , adjective Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
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Word Origin and History for homeomorphism n. 1854, from homeomorphous (1832), from homeo- + morphous (see metamorphosis ); originally of crystals. Homeomorphic is from 1902.

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Online Etymology Dictionary, © 2010 Douglas Harper

homeomorphism [hō′mē-ə-môr′ fĭz′əm]

A close similarity in the crystal forms of unlike compounds. A one-to-one correspondence between the points of two geometric figures such that open sets in the first geometric figure correspond to open sets in the second figure and conversely. If one figure can be transformed into another without tearing or folding, there exists a homeomorphism between them. Topological properties are defined on the basis of homeomorphisms. Show More

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