Please use this identifier to cite or link to this item:
Title: Computability of Polish spaces up to homeomorphism
Authors: Harrison-Trainor, Matthew
Melnikov, Alexander
Ng, Keng Meng
Keywords: Science::Mathematics
Issue Date: 2020
Source: Harrison-Trainor, M., Melnikov, A. & Ng, K. M. (2020). Computability of Polish spaces up to homeomorphism. Journal of Symbolic Logic, 85(4), 1664-1686.
Journal: Journal of Symbolic Logic
Abstract: We study computable Polish spaces and Polish groups up to homeomorphism. We prove a natural effective analogy of Stone duality, and we also develop an effective definability technique which works up to homeomorphism. As an application, we show that there is a Polish space not homeomorphic to a computable one. We apply our techniques to build, for any computable ordinal, an effectively closed set not homeomorphic to any -computable Polish space; this answers a question of Nies. We also prove analogous results for compact Polish groups and locally path-connected spaces.
ISSN: 0022-4812
DOI: 10.1017/jsl.2020.67
Rights: © 2020 The Association for Symbolic Logic. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

Citations 50

Updated on Dec 5, 2022

Web of ScienceTM
Citations 50

Updated on Dec 2, 2022

Page view(s)

Updated on Dec 6, 2022

Google ScholarTM




Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.