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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some properties of families of convex cones


Author: Meir Katchalski
Journal: Trans. Amer. Math. Soc. 233 (1977), 235-240
MSC: Primary 52A20
MathSciNet review: 0493755
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Abstract: The purpose of this paper is to study properties of finite families of convex cones in n-dimensional Euclidean space $ {R^n}$, whose members all have the origin as a common apex.

Of special interest are such families of convex cones in $ {R^n}$ which have the following property: Each member of the family is of dimension n, the intersection of any two members is at least $ (n - 1)$-dimensional, ..., the intersection of any n members is at least 1-dimensional and the intersection of all the members is the origin.


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

  • [1] M. J. C. Baker, A spherical Helly-type theorem, Pacific J. Math. 23 (1967), 1–3. MR 0222770 (36 #5820)
  • [2] B. Grünbaum, Convex polytopes, Interscience, New York, 1967. MR 37 #2085.
  • [3] M. Katchalski, Reconstructing dimensions of intersections of convex sets, Aequationes Math. 17 (1978), no. 2-3, 249–254. MR 0500552 (58 #18156)
  • [4] -, Non-degenerate families of convex cones and convex polytopes, Discrete Math. (to appear).
  • [5] -, On a Helfy type theorem of M. J. C. Baker, Proc. Amer. Math. Soc. (to appear).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0493755-3
PII: S 0002-9947(1977)0493755-3
Keywords: Euclidean space, convex sets
Article copyright: © Copyright 1977 American Mathematical Society