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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Characterizations of the generalized convex kernel
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by Arthur G. Sparks
Proc. Amer. Math. Soc. 27 (1971), 563-565
DOI: https://doi.org/10.1090/S0002-9939-1971-0279692-8

Abstract:

It is well known that the convex kernel $K$ of a set $S$ is the intersection of all maximal convex subsets of $S$. In this paper it is shown that the $n$th order kernel of a compact, simply-connected set $S$ in the plane is an ${L_n}$ set and is, in fact, the intersection of all maximal ${L_n}$ subsets of $S$. Furthermore, it is shown that one does not have to intersect the family of all the maximal ${L_n}$ subsets to obtain the $n$th order kernel, but that any subfamily thereof which covers the set is sufficient.
References
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Bibliographic Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 27 (1971), 563-565
  • MSC: Primary 52.30
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0279692-8
  • MathSciNet review: 0279692