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homeomorphism

 - 4 dictionary results

ho⋅me⋅o⋅mor⋅phism

  [hoh-mee-uh-mawr-fiz-uhm]
Use homeomorphism in a Sentence
–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.
Also called topological transformation.

Origin:
1850–55; homeomorph + -ism

Related forms:
ho⋅me⋅o⋅mor⋅phic, ho⋅me⋅o⋅mor⋅phous, adjective
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
Cite This Source Link To homeomorphism
ho·me·o·mor·phism   (hō'mē-ə-môr'fĭz'əm)   
n.  

  1. Chemistry A close similarity in the crystal forms of unlike compounds.

  2. Mathematics A continuous bijection between two figures whose inverse is also continuous.

ho'me·o·mor'phous adj.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Science Dictionary
homeomorphism   (hō'mē-ə-môr'fĭz'əm)  Pronunciation Key 

  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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Encyclopedia

homeomorphism

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 homeomorphism with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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