Compacta with Dense Ambiguous Loci of Metric Projections and Antiprojections

DOI10.2307/2161085zbMath0842.41024OpenAlexW4241269519MaRDI QIDQ4874194

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Publication date: 18 July 1996

Full work available at URL: https://doi.org/10.2307/2161085

zbMATH Keywords

metric projectionambiguous locusantiprojection

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (10)

Ambiguous loci of mutually nearest and mutually furthest points in Banach spaces ⋮ Ambiguous loci of the metric projection onto compact starshaped sets in a Banach space ⋮ Densely two-valued metric projections in uniformly convex Banach spaces ⋮ On an old theorem of Erd ⋮ Densely connected ambiguous loci of the metric projection in Hilbert spaces ⋮ The number of nearest and farthest points to a compactum in Euclidean space. ⋮ On generic well-posedness of restricted Chebyshev center problems in Banach spaces ⋮ Extending and paralleling Stechkin's category theorem ⋮ Farthest points and monotone operators ⋮ On well posedness of best simultaneous approximation problems in Banach spaces.

Cites Work

• The nearest point mapping is single valued nearly everywhere
• Farthest points in weakly compact sets
• Ambiguous loci of the nearest point mapping in Banach spaces
• Ambiguous loci of the metric projection onto compact starshaped sets in a Banach space
• Farthest points in reflexive locally uniformly rotund Banach spaces
• Existence Of Nearest Points In Banach Spaces
• Ambiguous loci of the farthest distance mapping from compact convex sets
• On compact connected sets in Banach spaces
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