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Proceedings of the American Mathematical Society

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

 
 

 

Intersecting unions of convex sets in $ R\sp{n}$


Author: Marilyn Breen
Journal: Proc. Amer. Math. Soc. 51 (1975), 427-431
MSC: Primary 52A35
DOI: https://doi.org/10.1090/S0002-9939-1975-0375088-2
MathSciNet review: 0375088
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Abstract: Let $ \mathcal{C} = \{ {C_\alpha }:\alpha $ in some index set $ I\} $ be a collection of convex sets, and let $ \mathfrak{M} = \{ {C_\alpha } \cup {C_\beta }:\alpha \ne \beta ,{C_\alpha },{C_\beta }$ in $ \mathcal{C}\} $. In this paper, various decomposition theorems are obtained for the set $ \cap \mathfrak{M}$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0375088-2
Keywords: Unions of convex sets, maximal convex subsets
Article copyright: © Copyright 1975 American Mathematical Society

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