Homomorphisms of minimal flows and generalizations of weak mixing

Abstract

In this paper we are concerned with generalizations of weakly mixing. Let : (X,T) -> (Y,T) be a homomorphism of metric minimal flows and let S() denote the relativized equicontinuous structure relation. The main result is that if has a RIM, , and z Z such that the support of z equals the fiber X o = ~ (z), then: