“…(3) For a metric spectral triple, (A, H , / D) the subgroup Iso(A,H , / D) defined by: By [12,Theorem 2.22], given an inductive sequence of quantum compact metric spaces, whose limit is a quantum compact metric space, we have that the existence of a special type of * -automorphism on the inductive limit which is well behaved with respect to the quantum metrics, called a bridge builder, is equivalent, under a very natural assumption, to the convergence of the given sequence of quantum compact metric spaces for the propinquity. Examples of such construction were noncommutative solenoids and bounded Bunce-Deddens algebras, see [12]. Now, given that (metric) spectral triples were thus enriched with their isometry groups structures, a natural question to ask was if one could extend the original bridge builder construction of [12] in such a way it insured the convergence of the associated isometry groups.…”