Mean dimension, small entropy factors and an embedding theorem

In this paper we show how the notion of mean dimension is connected in a natural way to the following two questions: what points in a dynamical system (X, T) can be distinguished by factors with arbitrarily small topological entropy, and when can a system (X, T) be embedded in (([0, 1] d ) Z , shift). Our results apply to extensions of minimalZ-actions, and for this case we also show that there is a very satisfying dimension theory for mean dimension.