Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections
@article{Brown2002LowerSC, title={Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections}, author={A. L. Brown and Frank Deutsch and V. Indumathi and Petar S. Kenderov}, journal={J. Approx. Theory}, year={2002}, volume={115}, pages={120-143} }
A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P"M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dimensional subspace has a continuous C"0(T) and L"1(@m) that have this property are determined.
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