Continuity and Lipschitz constants for projections
type: Item
instance of: scholarly article
title: Continuity and Lipschitz constants for projections
zbMATH Open document ID: 1185.41024
author: Douglas Bridges
published in: The Journal of Logic and Algebraic Programming
publication date: 2009-12-18T00:00:00Z
review text: Constructive proofs of some results from best approximation theory and properties of metric projections are given. For example, let \(Y\) be a locally compact subset of a complete metric space \(X\) such that each \(x \in X\) has a unique best approximation in \(Y\). Then the projection of \(X\) onto \(Y\) is sequentially continuous. Here, in order to prove sequential compactness of a complete totally bounded set, one needs to add the `limited principle of omniscience` (LPO) of intuitionistic logic.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 03F60
zbMATH DE Number: 5650086
zbMATH Keywords: constructive
zbMATH Keywords: best approximation
reviewed by: T.S.S.R.K. Rao
describes a project that uses: Nuprl
MaRDI profile type: Publication
full work available at URL: j.jlap.2009.02.002
OpenAlex ID: W2049747279
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DOI: 10.1016/J.JLAP.2009.02.002
description: scientific article; zbMATH DE number 5650086