Two Helly type theorems

Author:
Krzysztof Kołodziejczyk

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Two Helly type theorems for convex sets containing -dimensional half-flats are established, one of them being an extension of Katchalski's theorem [**3**] where the case was considered.

**[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**-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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0728359-7

Keywords:
Convex set,
-dimensional half-flat,
Helly's theorem

Article copyright:
© Copyright 1984
American Mathematical Society