International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 379-388
doi:10.1155/S0161171294000529

On distal and equicontinuous compact right topological groups

Abstract

W. Ruppert has studied, and given examples of, compact left topological groups for which the left translation flow (λG,G) is equicontinuous. Recently, we considered an analogous distal condition that applies to the groups of dynamical type; for these the topological centre is dense, so the translation flow is equicontinuous only in the trivial case when G is topological. In the present paper, we continue this work, exhibiting new characterizations of equicontinuity and distality of (λG,G); we also discuss examples and study some related matters.