Some properties of families of convex cones

The purpose of this paper is to study properties of finite families of convex cones in n-dimensional Euclidean space ${R^n}$, whose members all have the origin as a common apex.

Of special interest are such families of convex cones in ${R^n}$ which have the following property: Each member of the family is of dimension n, the intersection of any two members is at least $(n - 1)$-dimensional, ..., the intersection of any n members is at least 1-dimensional and the intersection of all the members is the origin.