Degrees of Non-computability of Homeomorphism Types of Polish Spaces

There are continuum many homeomorphism types of Polish spaces. In particular, there is a Polish space which is not homeomorphic to any computably presented Polish space. We examine the details of degrees of non-computability of presenting homeomorphic copies of Polish spaces.

Detalles Bibliográficos
Autores principales: Hoyrup, Mathieu, Kihara, Takayuki, Selivanov, Victor
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7309475/
http://dx.doi.org/10.1007/978-3-030-51466-2_16
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author Hoyrup, Mathieu
Kihara, Takayuki
Selivanov, Victor
author_facet Hoyrup, Mathieu
Kihara, Takayuki
Selivanov, Victor
author_sort Hoyrup, Mathieu
collection PubMed
description There are continuum many homeomorphism types of Polish spaces. In particular, there is a Polish space which is not homeomorphic to any computably presented Polish space. We examine the details of degrees of non-computability of presenting homeomorphic copies of Polish spaces.
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spelling pubmed-73094752020-06-23 Degrees of Non-computability of Homeomorphism Types of Polish Spaces Hoyrup, Mathieu Kihara, Takayuki Selivanov, Victor Beyond the Horizon of Computability Article There are continuum many homeomorphism types of Polish spaces. In particular, there is a Polish space which is not homeomorphic to any computably presented Polish space. We examine the details of degrees of non-computability of presenting homeomorphic copies of Polish spaces. 2020-06-24 /pmc/articles/PMC7309475/ http://dx.doi.org/10.1007/978-3-030-51466-2_16 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Hoyrup, Mathieu
Kihara, Takayuki
Selivanov, Victor
Degrees of Non-computability of Homeomorphism Types of Polish Spaces
title Degrees of Non-computability of Homeomorphism Types of Polish Spaces
title_full Degrees of Non-computability of Homeomorphism Types of Polish Spaces
title_fullStr Degrees of Non-computability of Homeomorphism Types of Polish Spaces
title_full_unstemmed Degrees of Non-computability of Homeomorphism Types of Polish Spaces
title_short Degrees of Non-computability of Homeomorphism Types of Polish Spaces
title_sort degrees of non-computability of homeomorphism types of polish spaces
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7309475/
http://dx.doi.org/10.1007/978-3-030-51466-2_16
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