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Finite unions of convex sets


Authors: J. F. Lawrence, W. R. Hare and John W. Kenelly
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0291952-4
Keywords: Unions of convex sets, convex kernel
Article copyright: © Copyright 1972 American Mathematical Society

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