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Lower semicontinuity, almost lower semicontinuity, and continuous selections for set-valued mappings. (English) Zbl 0653.41029
Let X be a paracompact space, Y a normed vector space and $2\sp Y$ the collection of all non-empty subsets of Y. A function f: $X\to 2\sp Y$ 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 $Y=C\sb 0(T)$ and $Y=L\sb 1$, the authors give intrinsic characterizations of the one-dimensional subspaces whose metric projections admit continuous selections.
Reviewer: H.R.Dowson

##### MSC:
 41A65 Abstract approximation theory
Full Text:
##### References:
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