Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Marilyn Breen, Intersecting unions of maximal convex sets, Proc. Amer. Math. Soc. 39 (1973), 587-590. MR 47 #7592. MR 0319046 (47:7592)
  • [2] Weir Katchalski, The dimension of intersections of convex sets, Israel J. Math. 10 (1971), 465-470. MR 46 #4367. MR 0305237 (46:4367)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 52A35

Retrieve articles in all journals with MSC: 52A35


Additional Information

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

American Mathematical Society