Weak heirs, coheirs and the Ellis semigroups

The paper’s Theorem 3.6 is stated and proved within a standing combinatorial set-up that ties A and B together via an embedding G ≺ H and a Boolean-algebra monomorphism A ↦ A# into B with B|G = A, yielding a continuous restriction map r: S(B) → S(A) used essentially in Lemma 2.14 and Corollary 2.11. Under these hypotheses, if every minimal left ideal in S(B) is a group, then each Ellis group of S(A) is isomorphic to a closed subgroup of an Ellis group of S(B) (Theorem 3.6, with Lemmas 3.7 and 3.8) . The candidate’s counterexample ignores these structural hypotheses, taking unrelated groups and algebras so that there is no #–embedding and no restriction map r; in particular, B|G ≠ A and G is not assumed to embed in H as required . Hence the model attempts to refute a stronger statement than the paper proves. The paper’s argument stands; the model’s counterexample is out of scope.