Journal of Convex Analysis 18 (2011), No. 2, 397--401
Copyright Heldermann Verlag 2011
A Note in Approximative Compactness and Continuity of Metric Projections in Banach Spaces
Antonio J. Guirao
Instituto de Matemática Pura y Aplicada, Universidad Politécnica, C/Vera s/n, 46022 Valencia, Spain
anguisa2@mat.upv.es
Vicente Montesinos
Instituto de Matemática Pura y Aplicada, Universidad Politécnica, C/Vera s/n, 46022 Valencia, Spain
vmontesinos@mat.upv.es
We give a counterexample to a recent statement in the metric approximation theory and provide a setting where the statement holds.
Keywords: Metric projection, approximative compactness, midpoint locally uniform rotundity, locally uniform rotundity, C-sets, proximinal sets.
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