Closed covers of compact convex polyhedra

Further generalizations of the Knaster-Kuratowski-Mazurkiewicz type theorems are presented. Also given is a new proof of David Gale's theorem on a family ofn closed covers of a simplex.The authors would like to thank Richard P. McLean for his valuable suggestions. A part of this paper was completed during Tatsuro Ichiishi's visit to Instytut Podstaw Informatyki, Polskiej Akademii Nauk (Polish Academy of Sciences), Warsaw, Poland, in early September 1990. Financial supports from the Polish Academy of Sciences and from the Ohio State University are gratefully acknowledged.