The complexity of the homeomorphism relation between compact metric spaces

Joseph Zielinski

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arXiv · 1409.5523

The complexity of the homeomorphism relation between compact metric spaces

Joseph Zielinski

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Abstract

We determine the exact complexity of classifying compact metric spaces up to homeomorphism. More precisely, the homeomorphism relation on compact metric spaces is Borel bi-reducible with the complete orbit equivalence relation of Polish group actions. Consequently, the same holds for the isomorphism relation between separable commutative C*-algebras and the isometry relation between C(K)-spaces.

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Joseph Zielinski. 2014-09-19. The complexity of the homeomorphism relation between compact metric spaces. https://arxiv.org/abs/1409.5523

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