Theory of representations
type: Item
instance of: scholarly article
title: Theory of representations
zbMATH Open document ID: 0588.03031
DOI: 10.1016/0304-3975(85)90208-7
author: Christoph Kreitz
author: Klaus Weihrauch
published in: Theoretical Computer Science
publication date: 1985-01-01T00:00:00Z
review text: An approach for a simple, general, and unified theory of effectivity on sets with cardinality not greater than that of the continuum is presented. A standard theory of effectivity on \({\mathbb{F}}=\{f:{\mathbb{N}}\to {\mathbb{N}}\}\) has been developed in a previous paper. By representations \(\delta\) :\({\mathbb{F}}\to M\) this theory is extended to other sets M. Topological and recursion theoretical properties of representations are studied, where the final topology of a representation plays an essential role. It is shown that for any separable \(T_ 0\)-space an (up to equivalence) unique admissible representation can be defined which reflects the topological properties correctly.
Mathematics Subject Classification ID: 03D65
Mathematics Subject Classification ID: 03D60
zbMATH DE Number: 3943802
zbMATH Keywords: type 2 computability
zbMATH Keywords: effectivity on sets
zbMATH Keywords: final topology of a representation
zbMATH Keywords: admissible representation
MaRDI profile type: Publication
full work available at URL: 0304-3975(85)90208-7
OpenAlex ID: W2168229531
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description: scientific article; zbMATH DE number 3943802