homeomorphism

homeomorphism

[hoh-mee-uh-mawr-fiz-uhm]
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:
1850–55; homeomorph + -ism

homeomorphic, homeomorphous, adjective
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Collins
World English Dictionary
homeomorphism or homoeomorphism (ˌhəʊmɪəˈmɔːfɪzəm)
 
n
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
 
homoeomorphism or homoeomorphism
 
n
 
homeo'morphic or homoeomorphism
 
adj
 
homeo'morphous or homoeomorphism
 
adj
 
homoeo'morphic or homoeomorphism
 
adj
 
homoeo'morphous or homoeomorphism
 
adj

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
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 Britannica
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.

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Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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