Interval functions related to geocze k-area^†

^†This research is partially supported by the National Science Foundation grant NSF GP-12915

Abstract

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 R^k which are topological K-cells. It is shown that the simplest interval is a polyhedral region in R^k whose complement is connected

^†This research is partially supported by the National Science Foundation grant NSF GP-12915

^†This research is partially supported by the National Science Foundation grant NSF GP-12915

Notes

^†This research is partially supported by the National Science Foundation grant NSF GP-12915