On idempotents in compact left topological universal algebras (Q2862920)

The paper deals with the generalization of Ellis' result to groupoids and topological groupoids. In the last section, left topological universal algebras with two binary operations are also considered. Two of the main results give sufficient conditions (given through some conditions for some terms of the universal algebra) for a left topological groupoid or a left topological universal algebra with two binary operations, to have an idempotent. There are also some results about the existence of sequences consisting of pairwise distinct elements and satisfying some extra conditions. However, these results are given without proofs (the reader is suggested to see another paper of the author for the proofs). For the main results, there are only sketches of the proofs. The paper also constains long (but useful) discussions about different conditions given in the main theorems and their essentiality.