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homeomorphism
[ hoh-mee-uh-mawr-fiz-uhm ]
/ ˌhoʊ mi əˈmɔr fɪz əm /
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noun
similarity in crystalline form but not necessarily in chemical composition.
Mathematics. a function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous.
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Also called topological transformation.
Origin of homeomorphism
First recorded in 1850–55; homeomorph + -ism
OTHER WORDS FROM homeomorphism
ho·me·o·mor·phic, ho·me·o·mor·phous, adjectiveWords nearby homeomorphism
Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2022
British Dictionary definitions for homeomorphism
homeomorphism
homoeomorphism
/ (ˌhəʊmɪəˈmɔːfɪzəm) /
noun
the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition
maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces
Derived forms of homeomorphism
homeomorphic, homeomorphous, homoeomorphic or homoeomorphous, adjectiveCollins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
Scientific definitions for homeomorphism
homeomorphism
[ hō′mē-ə-môr′fĭz′əm ]
A close similarity in the crystal forms of unlike compounds.
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
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