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Helly and Radon-type
theorems in interval convexity spaces
Phillip Wayne Bean |
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Vol. 51 (1974), No. 2, 363–368
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Abstract |
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The notion of interval convexity T on a point set S is defined. If T is an interval convexity defined on S,𝒞(T) will denote the collection of nonempty T-convex subsets of S. Properties k,H(k) (a Helly property), and R(k,n) (a Radon property) are defined on 𝒞(T), and relationships between these properties are investigated. A partial order convexity ≦ on a point set S is a special type of interval convexity. Some sufficient conditions are imposed on ≦ and 𝒞(≦) to insure the existence of certain Radon-type properties. |
Mathematical Subject Classification 2000
Primary: 52A35
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Milestones
Received: 13 February 1973
Revised: 11 November 1973
Published: 1 April 1974
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Authors |
| Phillip Wayne Bean | |
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