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oai:drops-oai.dagstuhl.de:11869 2024-03-06T10:48:53Z ddc:004 open_access

Descriptive Complexity on Non-Polish Spaces Callard, Antonin Hoyrup, Mathieu Represented space Computable analysis Descriptive set theory CoPolish spaces Represented spaces are the spaces on which computations can be performed. We investigate the descriptive complexity of sets in represented spaces. We prove that the standard representation of a countably-based space preserves the effective descriptive complexity of sets. We prove that some results from descriptive set theory on Polish spaces extend to arbitrary countably-based spaces. We study the larger class of coPolish spaces, showing that their representation does not always preserve the complexity of sets, and we relate this mismatch with the sequential aspects of the space. We study in particular the space of polynomials. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Antonin Callard and Mathieu Hoyrup 2020 Is Part Of LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2020.8 urn:nbn:de:0030-drops-118694 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.8 eng https://creativecommons.org/licenses/by/3.0/legalcode