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Degree Spectra of Homeomorphism Types of Polish Spaces

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 Polish spaces. We show that there exists a 0'-computable low3 Polish space which is not homeomorphic to a computable one, and that, for any natural number n, there exists a Polish space Xn such that exactly the high2n+3-degrees are required to present the homeomorphism type of Xn. We also show that no compact Polish space has an easiest presentation with respect to Turing reducibility.
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Contributor : Mathieu Hoyrup Connect in order to contact the contributor
Submitted on : Monday, April 27, 2020 - 10:06:45 AM
Last modification on : Friday, February 4, 2022 - 3:34:30 AM


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  • HAL Id : hal-02555111, version 1



Mathieu Hoyrup, Takayuki Kihara, Victor Selivanov. Degree Spectra of Homeomorphism Types of Polish Spaces. 2020. ⟨hal-02555111⟩



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