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On the topological aspects of the theory of represented spaces

Arno Pauly Orcid Logo

Computability, Volume: 5, Issue: 2, Pages: 159 - 180

Swansea University Author: Arno Pauly Orcid Logo

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DOI (Published version): 10.3233/COM-150049

Abstract

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented spaces is well-known to exhibit a strong topological flavour...

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Published in: Computability
ISSN: 22113568 22113576
Published: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa36015
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first_indexed 2017-10-11T13:17:32Z
last_indexed 2018-05-04T19:30:18Z
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spelling 2018-05-04T15:10:43.2309915 v2 36015 2017-10-11 On the topological aspects of the theory of represented spaces 17a56a78ec04e7fc47b7fe18394d7245 0000-0002-0173-3295 Arno Pauly Arno Pauly true false 2017-10-11 SCS Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented spaces is well-known to exhibit a strong topological flavour. We present an abstract and very succinct introduction to the field; drawing heavily on prior work by Escardo, Schroeder, and others.Central aspects of the theory are function spaces and various spaces of subsets derived from other represented spaces, and -- closely linked to these -- properties of represented spaces such as compactness, overtness and separation principles. Both the derived spaces and the properties are introduced by demanding the computability of certain mappings, and it is demonstrated that typically various interesting mappings induce the same property. Journal Article Computability 5 2 159 180 22113568 22113576 17 5 2016 2016-05-17 10.3233/COM-150049 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&amp;SrcAuth=ORCID&amp;SrcApp=OrcidOrg&amp;DestLinkType=FullRecord&amp;DestApp=WOS_CPL&amp;KeyUT=WOS:000376933200005&amp;KeyUID=WOS:000376933200005 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2018-05-04T15:10:43.2309915 2017-10-11T11:56:06.4745739 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Arno Pauly 0000-0002-0173-3295 1 0036015-12122017161927.pdf 2016-pauly-topologicalaspects.pdf 2017-12-12T16:19:27.6600000 Output 283354 application/pdf Version of Record true 2017-12-12T00:00:00.0000000 false eng
title On the topological aspects of the theory of represented spaces
spellingShingle On the topological aspects of the theory of represented spaces
Arno Pauly
title_short On the topological aspects of the theory of represented spaces
title_full On the topological aspects of the theory of represented spaces
title_fullStr On the topological aspects of the theory of represented spaces
title_full_unstemmed On the topological aspects of the theory of represented spaces
title_sort On the topological aspects of the theory of represented spaces
author_id_str_mv 17a56a78ec04e7fc47b7fe18394d7245
author_id_fullname_str_mv 17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly
author Arno Pauly
author2 Arno Pauly
format Journal article
container_title Computability
container_volume 5
container_issue 2
container_start_page 159
publishDate 2016
institution Swansea University
issn 22113568
22113576
doi_str_mv 10.3233/COM-150049
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
url http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&amp;SrcAuth=ORCID&amp;SrcApp=OrcidOrg&amp;DestLinkType=FullRecord&amp;DestApp=WOS_CPL&amp;KeyUT=WOS:000376933200005&amp;KeyUID=WOS:000376933200005
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description Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented spaces is well-known to exhibit a strong topological flavour. We present an abstract and very succinct introduction to the field; drawing heavily on prior work by Escardo, Schroeder, and others.Central aspects of the theory are function spaces and various spaces of subsets derived from other represented spaces, and -- closely linked to these -- properties of represented spaces such as compactness, overtness and separation principles. Both the derived spaces and the properties are introduced by demanding the computability of certain mappings, and it is demonstrated that typically various interesting mappings induce the same property.
published_date 2016-05-17T03:44:58Z
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score 11.035634

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