The Role of Complete Parts in Topological Polygroups
A topological polygroup is a polygroup P together with a topology on P such that the polygroup’s binary hyperoperation and the polygroup’s inverse function are continuous with respect to the topology. In this paper, we present some facts about complete parts in polygroups and we use these facts to obtain some new results in topological polygroups. We define the concept of cp-resolvable topological polygroups. A non-empty subset X of a topological polygroup is called cp-resolvable if there exist disjoint dense subsets A and B such that at least one of them is a complete part. Then, we investigate a few properties of cp-resolvable topological polygroups.