Journal article 874 views 272 downloads
On the topological aspects of the theory of represented spaces
Arno Pauly 
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 |
| Published: |
2016
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa36015 |
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| 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. 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
2 |
| Start Page: |
159 |
| End Page: |
180 |