homeomorphism


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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 topological spaces whose inverse is also continuous.

ho′me·o·mor′phic adj.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

homeomorphism

(ˌhəʊmɪəˈmɔːfɪzəm) or

homoeomorphism

n
1. (Chemistry) the property, shown by certain chemical compounds, of having the same crystal form but different chemical composition
2. (Mathematics) maths a one-to-one correspondence, continuous in both directions, between the points of two geometric figures or between two topological spaces
ˌhomeoˈmorphic, ˌhomeoˈmorphous, ˌhomoeoˈmorphic, ˌhomoeoˈmorphous adj
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

ho•me•o•mor•phism

(ˌhoʊ mi əˈmɔr fɪz əm)

n.
a mathematical function between two topological spaces that is continuous, one-to-one, and onto, and the inverse of which is continuous.
[1850–55]
ho`me•o•mor′phic, ho`me•o•mor′phous, adj.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.

homeomorphism

the similarity of the crystalline forms of substances that have different chemical compositions. — homeomorphous, adj.
See also: Physics
-Ologies & -Isms. Copyright 2008 The Gale Group, Inc. All rights reserved.
Translations
homeomorfihomøomorfi
homeomorfismi
homeomorfizam
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References in periodicals archive ?
* it is distinguished by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], i.e., any homeomorphism h : ([T.sup.1], [D.sub.o] + [D.sup.1]) [right arrow] ([T.sup.2], [D.sub.o] + [D.sup.2]) necessarily satisfies [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and
The mapping [[chi].sub.[DELTA]]: [M.sub.[DELTA]] [right arrow] [X.sub.[DELTA]] is a homeomorphism which is equivariant with respect to the actions of D3 and [D.sup.3.sub.C], respectively.
The nonlinear derivation operator is represented by an increasing homeomorphism [phi]: E [right arrow] E satisfying [phi]([theta]) = [theta] and such that [phi] is expansive, i.e.,
It is equivalent because the chaotic attractor differential in the two spaces is homeomorphism. The reconstructed system that includes the evolution information of all state variables is capable of calculating the future state of the system based on its current state, which provides a basic mechanism for chaotic time series prediction.
Let (X, f) and (Y, g) be compact spaces; we say f and g are topologically conjugate if there is a homeomorphism h : X [right arrow] Y, such that h [omicron] f = g [omicron] h.
Some sufficient conditions for assuring the existence, uniqueness, and exponential stability of the equilibrium point of the system are derived using the vector Lyapunov function method, homeomorphism mapping lemma, and the matrix theory.
Let f: (X, [tau]) [right arrow] (Y, [tau]) be a [theta]C homeomorphism and f (G) [contains not equal to] G'.
If there exists another regular curve [??]:[??] [right arrow] [G.sub.3] and a homeomorphism [sigma]: I [right arrow] [??] such that:
Two dynamical systems [([F.sub.t]).sub.t[greater than or equal to]0] and [([G.sub.t]).sub.t[greater than or equal to]0], where [F.sub.t] : X [right arrow] X and [G.sub.t] : Y [right arrow] Y; are topologically equivalent if there exists homeomorphism h : X [right arrow] Y, such that the following diagram is commutative:
By assumptions on T, h is a homeomorphism of Y onto X.
Also let the sets of coordinates be transformed so that the map becomes a homeomorphism of a class [C.sub.k].
Then there exists a [GAMMA] equivariant homeomorphism germ ([R.sup.2n] x R, (0,0)) [right arrow] ([R.sup.2n] x R, (0,0)) which maps the nonlinear normal modes of H to those of [H.sub.2] + [H.sub.k], preserving their symmetry groups.