The complexity of the homeomorphism relation between compact metric\n spaces

2014/09/19 by Joseph Zielinski, Zielinski, Joseph · 1 citation
Mathematics · #03E15 (Primary) #46L35 (Secondary) #54E45 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1409.5523

openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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