Compactness in constructive analysis revisited
type: Item
instance of: scholarly article
title: Compactness in constructive analysis revisited
zbMATH Open document ID: 0639.03060
DOI: 10.1016/0168-0072(87)90010-8
author: Christoph Kreitz
author: Klaus Weihrauch
published in: Annals of Pure and Applied Logic
publication date: 1987-01-01T00:00:00Z
review text: This paper, which follows other papers of the same authors, deals with constructive compactness. Representations of closed and compact subset of \({\mathbb{R}}\) are introduced and two different versions of the Heine-Borel theorem are proved. It is pointed out the fundamental role of topology in constructive analysis, and in particular of discontinuity as the main reason for nonconstructivity.
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03F65
Mathematics Subject Classification ID: 26A03
zbMATH DE Number: 4041912
zbMATH Keywords: constructive compactness
zbMATH Keywords: Heine-Borel theorem
zbMATH Keywords: topology
zbMATH Keywords: constructive analysis
zbMATH Keywords: discontinuity
reviewed by: Pier Luigi Ferrari
MaRDI profile type: Publication
full work available at URL: 0168-0072(87)90010-8
OpenAlex ID: W1967704436
cites work: Q3910522
cites work: Q5573965
cites work: Theory of representations
cites work: Discussion on: ``An optimal control approach for hybrid systems''
cites work: Type 2 recursion theory
cites work: Representations of the real numbers and of the open subsets of the set of real numbers
cites work: Q3751553
description: scientific article; zbMATH DE number 4041912