Continuity of metric projections onto subspaces and openness of quotient maps on unit balls

DOI10.1016/0021-9045(85)90042-5zbMath0582.41029OpenAlexW1975355109MaRDI QIDQ1069083

Jiří Reif

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0021-9045(85)90042-5

zbMATH Keywords

applicationsquotient mappointwise Lipschitz continuityproximinal linear subspacerelative openness

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (1)

A characterization of (locally) uniformly convex spaces in terms of relative openess of quotient maps on the unit ball

Cites Work

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• A remark on the lower semi-continuity of the set-valued metric projection
• Geometry of Banach spaces. Selected topics
• On the openness of the barycentre map
• On the geometry of stable compact convex sets
• Stable convex sets and extremal operators
• On the lower semicontinuity of the set-valued metric projection
• Smoothness of approximation
• Suns, moons, and quasi-polyhedra
• Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
• Best n -Dimensional Approximation to Sets of Functions
• Extension of compact operators
• The Existence and Unicity of Best Approximations.

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