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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Selection and representation theorems for $\sigma$-compact valued multifunctions
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by S. M. Srivastava PDF
Proc. Amer. Math. Soc. 83 (1981), 775-780 Request permission

Abstract:

In this paper we give two applications of results of Shchegolkov and Saint-Raymond on Borel sets with $\sigma$-compact sections. First we give a sufficient condition under which a partition of a Polish space into $\sigma$-compact sets admits a Borel cross-section. Then a representation theorem for $\sigma$-compact valued multifunctions, expressing them as unions of continuously indexed Borel graphs, is proved.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 83 (1981), 775-780
  • MSC: Primary 04A15; Secondary 04A05, 54C65, 54H05
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0630054-7
  • MathSciNet review: 630054