A Remark on Refinable Maps and Calmness

Abstract

Abstract.It is shown that if r : X -► Y is a refinable map between compacta and Y is calm, then r is a shape equivalence. As a corollary, if r : X -► Y is a refinable map between compacta and either X or Y is Sn-like (n > 1), then r is a shape equivalence, where Sn denotes the n-sphere.