Baire class 1 selectors for upper semicontinuous set-valued maps. (English) Zbl 0822.54017

Srivatsa, V. V.

Trans. Am. Math. Soc. 337, No. 2, 609-624 (1993).

Summary: Let \(T\) be a metric space and \(X\) a Banach space. Let \(F: T\to X\) be a set-valued map assuming arbitrary values and satisfying the upper semicontinuity condition: \(\{t\in T\): \(F(t)\cap C\neq \emptyset\}\) is closed for each weakly closed set \(C\) in \(X\). Then there is a sequence of norm-continuous functions converging pointwise (in the norm) to a selection for \(F\). We prove a statement of similar precision and generality when \(X\) is a metric space.

MSC:

54C65	Selections in general topology
46B99	Normed linear spaces and Banach spaces; Banach lattices
54C60	Set-valued maps in general topology

Keywords:

upper semicontinuous set-valued maps; Baire class 1 maps; selectors; weak topology; weak* topology

Citations:

Zbl 0822.54018