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- W4386874614 abstract "A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a $0'$-computable low$_3$ compact Polish space which is not homeomorphic to a computable one, and that, for any natural number $ngeq 2$, there exists a Polish space $X_n$ such that exactly the high$_{n}$-degrees are required to present the homeomorphism type of $X_n$. We also show that no compact Polish space has a least presentation with respect to Turing reducibility. The first version of this article appeared in April 2020. This version is a major update from September 2023, with improved proofs and results." @default.
- W4386874614 created "2023-09-20" @default.
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- W4386874614 date "2020-04-15" @default.
- W4386874614 modified "2023-09-27" @default.
- W4386874614 title "Degree spectra of homeomorphism types of compact Polish spaces" @default.
- W4386874614 doi "https://doi.org/10.48550/arxiv.2004.06872" @default.
- W4386874614 hasPublicationYear "2020" @default.
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