STRONG TOPOLOGICAL ROKHLIN PROPERTY, SHADOWING, AND SYMBOLIC DYNAMICS OF COUNTABLE GROUPS

The paper explicitly proves the equivalence: a countable group G has the strong topological Rokhlin property (STRP) if and only if for every n ≥ 2, projectively isolated subshifts are dense in SG(n) (Theorem 3.1) . The forward implication is established via a contrapositive Baire-category argument using continuity of the symbolic coding map Q(·,P) (Proposition 2.10) and Definition 2.22 of projectively isolated subshifts , while the reverse implication constructs a generic action as an inverse limit of projectively isolated subshifts satisfying a Fraïssé-style amalgamation scheme (Proposition 3.6) and shows its conjugacy class is dense Gδ (Propositions 3.8 and 3.9) . The candidate’s claim that the statement was “likely open as of cutoff” is therefore incorrect.