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Conference Paper/Proceeding/Abstract 11081 views 183 downloads

Noetherian Quasi-Polish spaces

Matthew de Brecht, Arno Pauly Orcid Logo

26th EACSL Annual Conference on Computer Science Logic (CSL 2017), Volume: 82

Swansea University Author: Arno Pauly Orcid Logo

DOI (Published version): 10.4230/LIPIcs.CSL.2017.16

Abstract

In the presence of suitable power spaces, compactness of X can be characterized as the singleton {X} being open in the space O(X) of open subsets of X. Equivalently, this means that universal quantification over a compact space preserves open predicates.Using the language of represented spaces, one...

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Published in: 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)
Published: Schloss Dagstuhl 2017
Online Access: http://drops.dagstuhl.de/opus/volltexte/2017/7698
URI: https://cronfa.swan.ac.uk/Record/cronfa37374
first_indexed 2017-12-12T13:49:46Z
last_indexed 2020-07-14T13:03:50Z
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spelling 2020-07-14T10:54:47.0194558 v2 37374 2017-12-08 Noetherian Quasi-Polish spaces 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2017-12-08 MACS In the presence of suitable power spaces, compactness of X can be characterized as the singleton {X} being open in the space O(X) of open subsets of X. Equivalently, this means that universal quantification over a compact space preserves open predicates.Using the language of represented spaces, one can make sense of notions such as a Σ02-subset of the space of Σ02-subsets of a given space. This suggests higher-order analogues to compactness: We can, e.g.~, investigate the spaces X where {X} is a Δ02-subset of the space of Δ02-subsets of X. Call this notion ∇-compactness. As Δ02 is self-dual, we find that both universal and existential quantifier over ∇-compact spaces preserve Δ02 predicates.Recall that a space is called Noetherian iff every subset is compact. Within the setting of Quasi-Polish spaces, we can fully characterize the ∇-compact spaces: A Quasi-Polish space is Noetherian iff it is ∇-compact. Note that the restriction to Quasi-Polish spaces is sufficiently general to include plenty of examples. Conference Paper/Proceeding/Abstract 26th EACSL Annual Conference on Computer Science Logic (CSL 2017) 82 Schloss Dagstuhl Quasi-Polish, synthetic topology, Noetherian space, finitely many mindchanges 31 12 2017 2017-12-31 10.4230/LIPIcs.CSL.2017.16 http://drops.dagstuhl.de/opus/volltexte/2017/7698 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2020-07-14T10:54:47.0194558 2017-12-08T13:10:20.8480397 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Matthew de Brecht 1 Arno Pauly 0000-0002-0173-3295 2 0037374-08122017141945.pdf 2017-pauly-debrecht-CSL.pdf 2017-12-08T14:19:45.8770000 Output 588148 application/pdf Version of Record true 2017-12-08T00:00:00.0000000 Published under a creative commons CC BY licence true eng
title Noetherian Quasi-Polish spaces
spellingShingle Noetherian Quasi-Polish spaces
Arno Pauly
title_short Noetherian Quasi-Polish spaces
title_full Noetherian Quasi-Polish spaces
title_fullStr Noetherian Quasi-Polish spaces
title_full_unstemmed Noetherian Quasi-Polish spaces
title_sort Noetherian Quasi-Polish spaces
author_id_str_mv 17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv 17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author Arno Pauly
author2 Matthew de Brecht
Arno Pauly
format Conference Paper/Proceeding/Abstract
container_title 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)
container_volume 82
publishDate 2017
institution Swansea University
doi_str_mv 10.4230/LIPIcs.CSL.2017.16
publisher Schloss Dagstuhl
college_str Faculty of Science and Engineering
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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
url http://drops.dagstuhl.de/opus/volltexte/2017/7698
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description In the presence of suitable power spaces, compactness of X can be characterized as the singleton {X} being open in the space O(X) of open subsets of X. Equivalently, this means that universal quantification over a compact space preserves open predicates.Using the language of represented spaces, one can make sense of notions such as a Σ02-subset of the space of Σ02-subsets of a given space. This suggests higher-order analogues to compactness: We can, e.g.~, investigate the spaces X where {X} is a Δ02-subset of the space of Δ02-subsets of X. Call this notion ∇-compactness. As Δ02 is self-dual, we find that both universal and existential quantifier over ∇-compact spaces preserve Δ02 predicates.Recall that a space is called Noetherian iff every subset is compact. Within the setting of Quasi-Polish spaces, we can fully characterize the ∇-compact spaces: A Quasi-Polish space is Noetherian iff it is ∇-compact. Note that the restriction to Quasi-Polish spaces is sufficiently general to include plenty of examples.
published_date 2017-12-31T04:15:38Z
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score 11.089572

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