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

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


Continuous Selections and Approximate Selection for Set-Valued Mappings and Applications to Metric Projections
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,
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