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• W3096756779 abstract "Abstract We study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that there is a $Delta ^0_2$ Polish space not homeomorphic to a computable one. We apply our techniques to build, for any computable ordinal $alpha $ , an effectively closed set not homeomorphic to any $0^{(alpha )}$ -computable Polish space; this answers a question of Nies. We also prove analogous results for compact Polish groups and locally path-connected spaces." @default.
• W3096756779 created "2020-11-09" @default.
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• W3096756779 date "2020-10-26" @default.
• W3096756779 modified "2023-10-17" @default.
• W3096756779 title "COMPUTABILITY OF POLISH SPACES UP TO HOMEOMORPHISM" @default.
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• W3096756779 doi "https://doi.org/10.1017/jsl.2020.67" @default.
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