Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings
Let X be a paracompact space, Y a normed vector space and \(2^ Y\) the collection of all non-empty subsets of Y. A function f: \(X\to 2^ Y\) is called a set-valued mapping. The relationships between lower semicontinuity, almost lower semicontinuity and the existence of various kinds of continuous selections for such a mapping are studied. For the cases \(Y=C_ 0(T)\) and \(Y=L_ 1\), the authors give intrinsic characterizations of the one-dimensional subspaces whose metric projections admit continuous selections.
scientific article; zbMATH DE number 4065598
scientific article