Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

  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},
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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