Chains without regularity

The paper proves that every compact dynamical system (no regularity on f) contains a closed, invariant, internally chain transitive subset, hence a C-transitive subsystem, via a constructive transfinite argument that avoids the Axiom of Choice (Theorem 3.9 and its proof) . It also notes that, when f is continuous, one can strengthen “C-transitive” to “minimal” . By contrast, the candidate solution assumes continuity to deduce dense orbits (and uses Zorn’s Lemma to produce a minimal set), thereby solving only the continuous case and relying on Choice, which the paper explicitly avoids; it does not address the general (possibly discontinuous) case demanded by the paper’s theorem. Hence the model’s proof does not solve the stated problem, while the paper’s argument is correct.