Set valued mappings, continuous selections, and metric projections

DOI10.1016/0021-9045(89)90083-XzbMath0675.41037MaRDI QIDQ1122075

Aldric L. Brown

Publication date: 1989

Published in: Journal of Approximation Theory (Search for Journal in Brave)

zbMATH Keywords

continuous selectionsmetric projectionsstable derived mapping

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (16)

On the nonuniqueness and instability of solutions of tracking-type optimal control problems ⋮ Stability estimates of continuous selections for metric almost-projections ⋮ Continuities of metric projection and geometric consequences ⋮ On continuity properties of the modulus of local contractibility ⋮ Robust maximization of asymptotic growth under covariance uncertainty ⋮ Bicommutants of multiplication operators ⋮ Continuous metric selection and multivariate approximation ⋮ Continuous selection theorems for nonlower semicontinuous multifunctions. ⋮ Metric projections after renorming ⋮ Concepts of lower semicontinuity and continuous selections for convex valued multifunctions ⋮ Selection theorems under an assumption weaker than lower semi-continuity ⋮ A comparative study of various notions of approximation of sets ⋮ On the topological entropy of continuous and almost continuous functions ⋮ On approximation properties of \(l_1\)-type spaces ⋮ Lower semicontinuity concepts, continuous selections, and set valued metric projections ⋮ Selections for quasi-l.s.c. mappings with uniformly equi-\(LC^ n\) range

Cites Work

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• On a theorem of Deutsch and Kenderov
• A continuity condition for the existence of a continuous selection for a set-valued mapping
• Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings
• The set of continuous selections of a metric projection in C(X)
• Continuous selections and finite-dimensional sets
• Continuous selections for metric projections
• Continuity of the set-valued metric projection
• On continuous selections for metric projections in spaces of continuous functions
• Selected Selection Theorems
• A survey of metric selections
• Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
• The Borsuk-Ulam Theorem and Orthogonality in Normed Linear Spaces
• Best n -Dimensional Approximation to Sets of Functions

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