homeomorphism

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

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.

Origin of homeomorphism

First recorded in 1850–55; homeomorph + -ism

Also called topological transformation.

Related formsho·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

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

Derived Formshomeomorphic, homeomorphous, homoeomorphic or homoeomorphous, adjective

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for homeomorphism

1854, from homeomorphous (1832), from homeo- + morphous (see metamorphosis); originally of crystals. Homeomorphic is from 1902.

homeomorphism in Science

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.