A characterization of the equicontinuous structure relation

Abstract

The main result in the paper is to show that in a large class of minimal transformation groups (including those with abelian phase groups, and point-distal transformation groups), the equicontinuous structure relation is precisely the regionally proximal relation. The techniques involved enable one to recover and extend the previously known characterizations. Several corollaries are indicated, among which the most important is a new criterion (which is easily applicable) for the existence of a nontrivial equicontinuous image of a given transformation group.