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Two Helly type theorems

Author: Krzysztof Kołodziejczyk
Journal: Proc. Amer. Math. Soc. 90 (1984), 412-414
MSC: Primary 52A35
MathSciNet review: 728359
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Abstract: Two Helly type theorems for convex sets containing $ k$-dimensional half-flats are established, one of them being an extension of Katchalski's theorem [3] where the case $ k = 1$ was considered.

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

  • [1] L. Danzer, B. Grünbaum and V. Klee, Helly's theorem and its relatives, Convexity, Proc. Sympos. Pure Math., Vol. 7, Amer. Math. Soc., Providence, R. I., pp. 101-180.
  • [2] R. de Santis, A generalization of Helly's theorem, Proc. Amer. Math. Soc. 8 (1957), 336-340. MR 0088748 (19:573e)
  • [3] M. Katchalski, A Helly type theorem for convex sets, Canad. Math. Bull. 21 (1978), 121-123. MR 0487796 (58:7400)
  • [4] A. G. Netrebin, Properties of systems of $ n$-dimensional convex sets in finite-dimensional linear spaces, Mat. Z. 25 (1979), 603-618; English transl., Math. Notes 25 (1979), 312-320. MR 534303 (80j:52004)

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Keywords: Convex set, $ k$-dimensional half-flat, Helly's theorem
Article copyright: © Copyright 1984 American Mathematical Society

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