Intersecting unions of convex sets in $R^{n}$
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- by Marilyn Breen PDF
- Proc. Amer. Math. Soc. 51 (1975), 427-431 Request permission
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 $\cap \mathfrak {M}$.References
- Marilyn Breen, Intersecting unions of maximal convex sets, Proc. Amer. Math. Soc. 39 (1973), 587–590. MR 319046, DOI 10.1090/S0002-9939-1973-0319046-0
- Meir Katchalski, The dimension of intersections of convex sets, Israel J. Math. 10 (1971), 465–470. MR 305237, DOI 10.1007/BF02771734
Additional Information
- © Copyright 1975 American Mathematical Society
- 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