Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings

@article{Deutsch1988LowerSA,
  title={Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings},
  author={Frank Deutsch and V. Indumathi and Klaus Schnatz},
  journal={Journal of Approximation Theory},
  year={1988},
  volume={53},
  pages={266-294}
}
Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections
TLDR
A number of semicontinuity concepts and the relations between them are discussed and 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).
Continuous Selections For Almost Lower Semicontinuous Multifunctions
In this paper, we obtain several new continuous selection theorems for almost lower semicontinuous multifunctions T on a paracompact topological space X, in the general noncompact and/or nonconvex
Michael selection theorem under weak lower semicontinuity assumption
We give a continuous selection theorem for convex-valued multifunctions satisfying slightly weaker lower semicontinuity assumptions than those which are adopted in the famous Michael Theorem [4] and
Selections For Metric Projections
A review is given of conditions which characterise when the metric projection onto a proximinal subspace of a normed linear space has a selection which is continuous, (pointwise) Lipschitz
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