Vol. 51, No. 2, 1974

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Helly and Radon-type theorems in interval convexity spaces

Phillip Wayne Bean

Vol. 51 (1974), No. 2, 363–368

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
Received: 13 February 1973
Revised: 11 November 1973
Published: 1 April 1974
Phillip Wayne Bean