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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A selection theorem for multifunctions
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by H. Sarbadhikari PDF
Proc. Amer. Math. Soc. 71 (1978), 285-288 Request permission

Abstract:

In this paper the following theorem is proved. X is any set, H is a family of subsets of X which is $\lambda$-additive, $\lambda$-multiplicative and satisfies the $\lambda$-WRP for some cardinal $\lambda > {\aleph _0}$. Suppose Y is a regular Hausdorff space of topological weight $\leqslant \lambda$ such that given any family of open sets, there is a subfamily of cardinality $< \lambda$ with the same union. Let $F:X \to {\mathbf {C}}(Y)$, where ${\mathbf {C}}(Y)$ is the family of nonempty compact subsets of Y, satisfy $\{ x:F(x) \cap C \ne \emptyset \} \in {\mathbf {H}}$ for any closed subset C of Y. Then F admits a ${({\mathbf {H}} \cap {{\mathbf {H}}^c})_\lambda }$ measurable selector.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 71 (1978), 285-288
  • MSC: Primary 54C65; Secondary 04A20, 54A25, 54C60
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0500507-0
  • MathSciNet review: 500507