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homeomorphism

[hoh-mee-uh-mawr-fiz-uh m] /ˌhoʊ mi əˈmɔr fɪz əm/
noun
1.
similarity in crystalline form but not necessarily in chemical composition.
2.
Mathematics. a function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous.
Origin
1850-1855
1850-55; homeomorph + -ism
Related forms
homeomorphic, homeomorphous, adjective
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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British Dictionary definitions for homeomorphic

homeomorphism

/ˌhəʊmɪəˈmɔːfɪzəm/
noun
1.
the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition
2.
(maths) a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces
Derived Forms
homeomorphic, homeomorphous, homoeomorphic, 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
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Word Origin and History for homeomorphic

homeomorphism

n.

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

Online Etymology Dictionary, © 2010 Douglas Harper
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homeomorphic in Science
homeomorphism
  (hō'mē-ə-môr'fĭz'əm)   
  1. A close similarity in the crystal forms of unlike compounds.

  2. 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.


The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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