Helly and Radon-type theorems in interval convexity spaces
Phillip Bean · Pacific Journal of Mathematics · 1974
The notion of interval convexity Ton a point set S is defined. If T is an interval convexity defined on S, &(T) will denote the collection of nonempty T-convex subsets of S. Properties k, H(k) (a Helly property), and R(h, n) (a Radon property) are defined on ^(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 g and &(£) to insure the existence of certain Radon-type properties.