Onl-simplicial convexity in vector spaces

Abstract

The paper is concerned with a generalized type of convexity, which is called /-simplicial convexity.The name is derived from the simplex with I vertices, an Z-simplicial convex set being the union of all (ΐ -l)-simplexes with vertices in another set, i varying between 1 and I.The basic space is a linear one.For convex sets the Z-order (which is a natural number associated to an ί-simplicial convex set) is a decreasing function of I. Several inequalities between I-and ά-orders are established.In doing this the case of a convex set and that of a non convex set are distinguished.Besides these inequalities, the main result of the paper is the proof of non monotonicity of the border, given by an example in a 34-dimensional linear space.

Locations

• Pacific Journal of Mathematics - View - PDF