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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Finite unions of convex sets
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by J. F. Lawrence, W. R. Hare and John W. Kenelly PDF
Proc. Amer. Math. Soc. 34 (1972), 225-228 Request permission

Abstract:

In this paper it is shown that a set is the union of k convex subsets if and only if every finite subset of it is contained in some k convex subsets of it. This is a characterization of a set as the union of a finite number of convex sets by conditions on its finite subsets. Also, a proof of McKinney’s theorem for unions of two convex sets is given using similar methods.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 225-228
  • MSC: Primary 52A05; Secondary 46A15
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0291952-4
  • MathSciNet review: 0291952