GENERICITY OF DISTRIBUTIONAL CHAOS IN NON-AUTONOMOUS SYSTEMS

The paper claims DC1-density in Fp(I) “independently of the metric we use,” and sketches a proof by splitting metrics into two large classes and, for the ‘integral-type’ class, forming ‘linear combinations’ with the limit map. Both moves are flawed as stated: (i) the metric-independence is false for pathologies such as the discrete metric on Cs(I), where ρF-balls of radius <1 are singletons, so DC1 cannot be dense and every subset is both open and closed; yet the paper asserts independence of the chosen metric for density and for (non-)openness/closedness. (ii) The proof asserts convex combinations of two continuous surjective I→I maps are again surjective, which is incorrect. By contrast, the model restricts to admissible metrics (topologically equivalent to ρsup), supplies a standard proximal/separation block construction that preserves surjectivity (via anchored preimages) and C0-smallness, and correctly recovers DC1-density as a topological statement invariant under metric equivalence. On Cantor space Q and on non-openness/non-closedness, both paper and model agree in substance.