Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings
type: Item
instance of: scholarly article
title: Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings
zbMATH Open document ID: 0653.41029
DOI: 10.1016/0021-9045(88)90023-8
author: F. Deutsch
author: V. Indumathi
author: Klaus Schnatz
published in: Journal of Approximation Theory
publication date: 1988-01-01T00:00:00Z
review text: Let X be a paracompact space, Y a normed vector space and \(2^ Y\) the collection of all non-empty subsets of Y. A function f: \(X\to 2^ Y\) is called a set-valued mapping. The relationships between lower semicontinuity, almost lower semicontinuity and the existence of various kinds of continuous selections for such a mapping are studied. For the cases \(Y=C_ 0(T)\) and \(Y=L_ 1\), the authors give intrinsic characterizations of the one-dimensional subspaces whose metric projections admit continuous selections.
Mathematics Subject Classification ID: 41A65
zbMATH DE Number: 4065598
zbMATH Keywords: lower semicontinuity
zbMATH Keywords: almost lower semicontinuity
zbMATH Keywords: metric projections
zbMATH Keywords: continuous selections
reviewed by: H. R. Dowson
MaRDI profile type: Publication
full work available at URL: 0021-9045(88)90023-8
OpenAlex ID: W1982995731
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description: scientific article; zbMATH DE number 4065598