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Overt choice

Matthew de Brecht, Arno Pauly Orcid Logo, Matthias Schröder

Computability, Volume: 9, Issue: 3-4, Pages: 169 - 191

Swansea University Author: Arno Pauly Orcid Logo

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DOI (Published version): 10.3233/com-190253

Abstract

We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice is continuous for a given space is related t...

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Published in: Computability
ISSN: 2211-3568 2211-3576
Published: IOS Press 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa53986
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first_indexed 2020-04-18T19:46:06Z
last_indexed 2023-01-11T14:31:49Z
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spelling 2022-12-05T12:53:21.5359615 v2 53986 2020-04-18 Overt choice 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2020-04-18 SCS We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice is continuous for a given space is related to topological completeness notions such as the Choquet-property; and to whether variants of Michael’s selection theorem hold for that space. For spaces where overt choice is discontinuous it is interesting to explore the resulting Weihrauch degrees, which in turn are related to whether or not the space is Fréchet–Urysohn. Journal Article Computability 9 3-4 169 191 IOS Press 2211-3568 2211-3576 Weihrauch reducibility, computable topology, quasi-Polish space 3 8 2020 2020-08-03 10.3233/com-190253 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2022-12-05T12:53:21.5359615 2020-04-18T18:52:56.3921628 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Matthew de Brecht 1 Arno Pauly 0000-0002-0173-3295 2 Matthias Schröder 3 53986__17277__ef0e7cf9bdf646d2b97f181bf686d3e4.pdf 1902.05926.pdf 2020-05-18T13:36:31.2510435 Output 553688 application/pdf Accepted Manuscript true false
title Overt choice
spellingShingle Overt choice
Arno Pauly
title_short Overt choice
title_full Overt choice
title_fullStr Overt choice
title_full_unstemmed Overt choice
title_sort Overt choice
author_id_str_mv 17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv 17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author Arno Pauly
author2 Matthew de Brecht
Arno Pauly
Matthias Schröder
format Journal article
container_title Computability
container_volume 9
container_issue 3-4
container_start_page 169
publishDate 2020
institution Swansea University
issn 2211-3568
2211-3576
doi_str_mv 10.3233/com-190253
publisher IOS Press
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description We introduce and study the notion of overt choice for countably-based spaces and for CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by what open sets intersect it. We show that the question of whether overt choice is continuous for a given space is related to topological completeness notions such as the Choquet-property; and to whether variants of Michael’s selection theorem hold for that space. For spaces where overt choice is discontinuous it is interesting to explore the resulting Weihrauch degrees, which in turn are related to whether or not the space is Fréchet–Urysohn.
published_date 2020-08-03T04:07:15Z
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score 11.013776

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