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

noun 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.

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. 2019

British Dictionary definitions for homeomorphic

homeomorphism homoeomorphism

noun 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

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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 homeomorphic 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

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.

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