“…For topological dimension zero, assuming A is separable, the chain of implications is the same, but now uses, in the same order as above, Theorem 3.6 of [19], Theorem 3.17 of [17], Lemma 3.3 of [17], and [24]. When G is a finite abelian 2-group, all the properties under consideration have the form "residually hereditarily in an upwards directed class of C*-algebras", and we use the same reasoning, now applying, in order, Theorem 3.2(ii) of [19], Corollary 3.3(ii) of [19], Proposition 5.10(2) of [18], and [24]. We expect the restriction to 2-groups to be unnecessary.…”