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On the topological aspects of the theory of represented spaces
Computability, Volume: 5, Issue: 2, Pages: 159 - 180
Swansea University Author:
Arno Pauly
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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...
Published in: | Computability |
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ISSN: | 22113568 22113576 |
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2016
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URI: | https://cronfa.swan.ac.uk/Record/cronfa36015 |
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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&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000376933200005&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 |
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17a56a78ec04e7fc47b7fe18394d7245 |
author_id_fullname_str_mv |
17a56a78ec04e7fc47b7fe18394d7245_***_Arno Pauly |
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Arno Pauly |
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Arno Pauly |
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Journal article |
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Computability |
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5 |
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159 |
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2016 |
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Swansea University |
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22113568 22113576 |
doi_str_mv |
10.3233/COM-150049 |
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Faculty of Science and Engineering |
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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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1763752121562300416 |
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11.021648 |