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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.


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
“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

homeomorphism

/ hō′mē-ə-môrfĭz′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.
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Derived Forms

  • ˌhomeoˈmorphic, adjective
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Other Words From

  • home·o·morphic home·o·morphous adjective
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Word History and Origins

Origin of homeomorphism1

First recorded in 1850–55; homeomorph + -ism
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Example Sentences

Homeomorphism is one version of equivalence.

We can see that these spaces don’t have this stronger ambient homeomorphism by looking at what happens around them.

This is called ambient homeomorphism.

We could request this continuous function from one mathematical object to another with a continuous inverse also be a homeomorphism of the ambient space around the two objects, which basically mean it doesn't just have to be nice to the mathematical object but to the entire universe the object lives in.

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homeomorph“Home on the Range”