follow Dictionary.com

Your favorite word could be our Word of the Day!

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.
Cite This Source
British Dictionary definitions for homeomorphism

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
Cite This Source
Word Origin and History for homeomorphism
n.

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

Online Etymology Dictionary, © 2010 Douglas Harper
Cite This Source
homeomorphism 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.
Cite This Source
Encyclopedia Article for homeomorphism

bicontinuous function

in mathematics, a correspondence between two figures or surfaces or other geometrical objects, defined by a one-to-one mapping that is continuous in both directions. The vertical projection shown in the sets up such a one-to-one correspondence between the straight segment x and the curved interval y. If x and y are topologically equivalent, there is a function h:xy such that h is continuous, h is onto (each point of y corresponds to a point of x), h is one-to-one, and the inverse function, h1, is continuous. Thus h is called a homeomorphism.

Learn more about bicontinuous function with a free trial on Britannica.com
Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
Cite This Source

Word of the Day

Difficulty index for homeomorphism

Few English speakers likely know this word

Word Value for homeomorphism

27
0
Scrabble Words With Friends

Nearby words for homeomorphism