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A Helly type theorem on the sphere

Author: Meir Katchalski
Journal: Proc. Amer. Math. Soc. 66 (1977), 119-122
MSC: Primary 52A35
MathSciNet review: 0470868
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Abstract: This paper establishes a Helly type theorem for convex sets in $ {S_n}$, the n-dimensional unit sphere.

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 36 #5820. MR 0222770 (36:5820)
  • [2] L. Danzer, B. Grünbaum and V. Klee, Helly's theorem and its relatives, Proc. Sympos. Pure Math., vol. 7, Amer. Math. Soc., Providence, R. I., 1963, pp. 101-180. MR 28 #524.
  • [3] B. Grünbaum, Convex polytopes, Interscience, New York, 1967. MR 37 #2085.
  • [4] M. Katchalski, Some properties of families of convex cones, Trans. Amer. Math. Soc. (to appear). MR 0493755 (58:12724)
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Keywords: Convex sets, n-dimensional unit sphere, Helly type theorems
Article copyright: © Copyright 1977 American Mathematical Society

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