Remote Access Transactions of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9947-1993-1140919-0
MathSciNet review: 1140919
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54C60, 47H04, 49J45, 54C65

Retrieve articles in all journals with MSC: 54C60, 47H04, 49J45, 54C65


Additional Information

Keywords: Upper semicontinuous set-valued maps, Baire class <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$1$"> maps, selectors, weak and <!– MATH ${\text {weak}^\ast }$ –> <IMG WIDTH="58" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img11.gif" ALT="${\text {weak}^\ast }$"> topologies
Article copyright: © Copyright 1993 American Mathematical Society