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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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https://hal.inria.fr/hal-02555111
Contributor : Mathieu Hoyrup <>
Submitted on : Monday, April 27, 2020 - 10:06:45 AM
Last modification on : Friday, January 22, 2021 - 10:40:45 AM

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  • HAL Id : hal-02555111, version 1

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

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