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- n. Plural form of homeomorphism.
Sorry, no etymologies found.
The widespread existence of homeomorphisms, which are not defined in terms of evolution, can be used as evidence for evolution.
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).
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.
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.