Representations of the real numbers and of the open subsets of the set of real numbers
type: Item
instance of: scholarly article
title: Representations of the real numbers and of the open subsets of the set of real numbers
zbMATH Open document ID: 0643.03041
DOI: 10.1016/0168-0072(87)90065-0
author: Christoph Kreitz
author: Klaus Weihrauch
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
review text: In previous papers the authors have presented a unified type 2 theory of computability and continuity and a theory of representations. In this paper the concepts developed so far are used for the foundation of a new kind of constructive analysis. Different standard representations of the real numbers are compared. It turns out that the crucial differences are of topological nature and that most of the representations (e.g., the decimal representation) are not reasonable for topological reasons. In the second part some effective representations of the open subsets of the real numbers are introduced and compared.
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03F65
Mathematics Subject Classification ID: 03D45
Mathematics Subject Classification ID: 03D65
zbMATH DE Number: 4047714
zbMATH Keywords: admissible representations
zbMATH Keywords: constructive analysis
zbMATH Keywords: representations of the real numbers
MaRDI profile type: Publication
full work available at URL: 0168-0072(87)90065-0
OpenAlex ID: W1977390449
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description: scientific article; zbMATH DE number 4047714