Proximality and regional proximality in minimal flows (Q1765985)

Here, a flow is a jointly continuous action of a topological group on a compact Hausdorff space. A number of facts about proximal relation \(P\) and regionally proximal relation \(Q\) are obtained. Among others, the question is investigated under which conditions \(P\) is an equivalence relation. The property ``\(P\) is an equivalence relation'' is preserved under factors. Necessary and sufficient conditions for this property to be lifted by a homomorphism of flows are found. Further, the question is investigated under which conditions the product relation \(QP\) is the equicontinuous structure relation of a minimal flow. Some other results, examples and remarks are added.