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}
}
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23 Citations
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23 Citations

Concepts of lower semicontinuity and continuous selections for convex valued multifunctions
Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections
TLDR
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Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces
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…
Generalized selection theorems without convexity
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References

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Two new continuity properties for set-valued mappings are defined which are weaker than lower semicontinuity. One of these properties characterizes when approximate selections exist. A few selection…
Continuous selections in Chebyshev approximation
A survey on continuous selections for the set-valued metric projection onto finite-dimensional subspaces of C[a,b] is given. Some applications are discussed.
Characterization of the space of continuous functions over a compact Hausdorff space
1. This paper consists of two parts, in each of which is established a completely characteristic property of those Banach spaces which are, as Banach spaces, the class of all continuous, bounded,…
A remark on the lower semi-continuity of the set-valued metric projection
On some geometric properties of suns
Zur Stetigkeit von mengenwertigen metrischen Projektionen
Vor einigen Jahren stellte V. Klee [11] das Problem »Unter welchen Bedingungen hat eine Cebysev-Menge A in einem normierten Vektorraum X eine stetige metrische Projektion (i. e. die Abbildung, die…
Continuous Selections. I
Best n‐Dimensional Approximation to Sets of Functions
Continuous selections for metric projections
On the lower semicontinuity of the set-valued metric projection
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