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Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. Plural form of homeomorphism.

Etymologies

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Examples

  • The widespread existence of homeomorphisms, which are not defined in terms of evolution, can be used as evidence for evolution.

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  • However, it is possible to prove the Loomis-Sikorski representation theorem without choice; see for instance canonical, but it is not unique (in contrast to the situation with the Stone representation theorem, where Lemma 1 provides uniqueness up to homeomorphisms).

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  • The important difference between a differentiable manifold and a topological manifold is that the charts are diffeomorphisms (a differentiable function with a differentiable inverse) rather than homeomorphisms.

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  • In a more general setting there are three of these E_8’s: one the chiral dual to the first E_8 and the third an exceptional group required to define homeomorphisms over all four-manifolds that are configuration variables for quantum gravity states.

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