Togo Nishiura

Interval functions related to geocze k-area†

The Geocze area theory for dimension two uses the geometrically simplest intervals on which area theory can he developed, These intervals are simple polygonal regions in the plane. For Geocze k-area with k > 2 it is shown in the present paper that the geometrically simplest interval arc not tue obvious generalizations of the- two dimensional case, that is, polyhedral regions in Rk which are topological K-cells. It is shown that the simplest interval is a polyhedral region in Rk whose complement is connected