Two Helly type theorems
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- by Krzysztof Kołodziejczyk PDF
- Proc. Amer. Math. Soc. 90 (1984), 412-414 Request permission
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
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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.
- Richard De Santis, A generalization of Helly’s theorem, Proc. Amer. Math. Soc. 8 (1957), 336–340. MR 88748, DOI 10.1090/S0002-9939-1957-0088748-7
- Meir Katchalski, A Helly-type theorem for convex sets, Canad. Math. Bull. 21 (1978), no. 1, 121–123. MR 487796, DOI 10.4153/CMB-1978-021-5
- A. G. Netrebin, Properties of systems of $n$-dimensional convex sets in finite-dimensional linear spaces, Mat. Zametki 25 (1979), no. 4, 603–618, 637 (Russian). MR 534303
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 412-414
- MSC: Primary 52A35
- DOI: https://doi.org/10.1090/S0002-9939-1984-0728359-7
- MathSciNet review: 728359