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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Baire class $ 1$ selectors for upper semicontinuous set-valued maps


Author: V. V. Srivatsa
Journal: Trans. Amer. Math. Soc. 337 (1993), 609-624
MSC: Primary 54C60; Secondary 47H04, 49J45, 54C65
MathSciNet review: 1140919
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Abstract: 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 \ne \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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1140919-0
PII: S 0002-9947(1993)1140919-0
Keywords: Upper semicontinuous set-valued maps, Baire class $ 1$ maps, selectors, weak and $ {\text{weak}^\ast}$ topologies
Article copyright: © Copyright 1993 American Mathematical Society