# 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} }

## 23 Citations

Concepts of lower semicontinuity and continuous selections for convex valued multifunctions

- Mathematics
- 1992

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

- MathematicsJ. Approx. Theory
- 2002

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

- Mathematics
- 2011

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

- Mathematics
- 1990

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…

Strong uniqueness, Lipschitz continuity, and continuous selections for metric projections

- Mathematics
- 1991

Characterizations of continuous and Lipschitz continuous metric selections in normed linear spaces

- Mathematics, Computer Science
- 1989

Selections For Metric Projections

- Mathematics
- 1992

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…

## References

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- Mathematics
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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

- Mathematics
- 1984

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

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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,…

Zur Stetigkeit von mengenwertigen metrischen Projektionen

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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…