On distal and equicontinuous compact right topological groups
R. Ellis showed that a flow on a compact space is distal if and only if its enveloping semigroup is a group. However, rather surprisingly, if \(G\) is a compact left-topological group then the flow on \(G\) consisting of left translations need be neither distal nor equicontinuous. It is shown that the flow on \(G\) is distal resp. equicontinuous if and only if every continuous function on \(G\) is distal resp. almost periodic. The paper then goes on to try to determine the set of continuous almost periodic functions on \(G\). Solutions are found when \(G\) has dense topological centre, but the situation is shown to be complicated in general.
scientific article; zbMATH DE number 569407