The structure of weakly mixing minimal transformation groups

Abstract

KEYNESdense.When Z is metric, this is equivalent to hving point with dense orbit (point-transitive).Also, (Z, T, p) is weakly mixing (i.e., (Z, T, p) if (Z Z, T, p X p) e g.Since weakly mixing and minimlity re inde- pendent of the topology on T, we assume unless otherwise stated that T is discrete.If T has non-trivial topological group topology, then p is ssumed continuous.We will frequently surpress p. Finally, we denote suriecrive transformation group homomorphism from (Z, T) to nother trans- formation group (W, T) by (Z, T) --+ (W, T).We shall assume familiarity with the algebraic theory of point-transitive transformation groups.See [1, or [3] for general reference and for notation.We will use extensively the notion of quasi-separable

Locations

• Illinois Journal of Mathematics - View - PDF