The complexity of the homeomorphism relation between compact metric spaces
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...
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| creator | Zielinski, Joseph |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.1409.5523 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.1409.5523</identifier><language>eng</language><subject>Mathematics - Functional Analysis ; Mathematics - Logic</subject><creationdate>2014-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1409.5523$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1409.5523$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Zielinski, Joseph</creatorcontrib><title>The complexity of the homeomorphism relation between compact metric spaces</title><description>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
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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.</abstract><doi>10.48550/arxiv.1409.5523</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Functional Analysis Mathematics - Logic |
| title | The complexity of the homeomorphism relation between compact metric spaces |
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