Definitions
from The American Heritage® Dictionary of the English Language, 5th Edition.
- noun Chemistry A close similarity in the crystal forms of unlike compounds.
- noun Mathematics A continuous bijection between two topological spaces whose inverse is also continuous.
from The Century Dictionary.
- noun Similarity in crystalline form, but not necessarily in chemical composition.
- noun Same as
isomorphism . - noun Also
homeomorphism .
from the GNU version of the Collaborative International Dictionary of English.
- noun A near similarity of crystalline forms between unlike chemical compounds. See
isomorphism .
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun topology a
continuous bijection from onetopological space to another, with continuousinverse . - noun chemistry a
similarity in thecrystal structure ofunrelated compounds
Etymologies
from Wiktionary, Creative Commons Attribution/Share-Alike License
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Examples
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A homeomorphism is, essentially, a one-to-one correspondence (see any maths site for details).
On Thursday, the Legg report will be published along with... 2008
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One is that it is a homeomorphism invariant: if two spaces are homeomorphic, then they have the same fundamental group.
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One is that it is a homeomorphism invariant: if two spaces are homeomorphic, then they have the same fundamental group.
Conservapedia - Recent changes [en] PatrickD 2009
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One is that it is a homeomorphism invariant: if two spaces are homeomorphic, then they have the same fundamental group.
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The topology on the countable product of the two-point space '' D '' is induced by the metric The Cantor set may be embedded in the unit interval by the map which is a homeomorphism onto the subset of the unit interval obtained by iteratively deleting the middle third of each interval compact.
Citizendium, the Citizens' Compendium - Recent changes [en] 2008
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The Cantor set is [[homeomorphism | homeomorphic]] to a product of [[countable set | countably]] many copies of a two-point space with the [[discrete metric]].
Citizendium, the Citizens' Compendium - Recent changes [en] 2008
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While the existence of a homeomorphism between manifolds demonstrates the existence of a diffeomorphism between them if they are of dimension it is possible to construct objects which are homeomorphic and not diffeomorphic - such objects are called "exotic
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While the existence of a homeomorphism between manifolds demonstrates the existence of a diffeomorphism between them if they are of dimension it is possible to construct objects which are homeomorphic and not diffeomorphic - such objects are called "exotic
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