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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Selection theorems and the reduction principle


Authors: A. Maitra and B. V. Rao
Journal: Trans. Amer. Math. Soc. 202 (1975), 57-66
MSC: Primary 54C65
DOI: https://doi.org/10.1090/S0002-9947-1975-0355960-4
MathSciNet review: 0355960
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Abstract: In this paper we attempt a unification of several selection theorems in the literature. It is proved that the existence of ``nice'' selectors in a certain class of selection problems is essentially equivalent to the fact that certain families of sets satisfy a weak version of Kuratowski's reduction principle. Various special cases are discussed.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0355960-4
Keywords: Set-valued maps, selections, reduction principle
Article copyright: © Copyright 1975 American Mathematical Society

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