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We introduce a topology on the ideal space of inductive limits of C*-algebrasbuilt by a topological inverse limit of the Fell topologies on the C*-algebrasof the given inductive sequence and we produce conditions for when thistopology agrees with the Fell topology of the inductive limit. With thistopology, we impart criteria for when convergence of ideals of an AF algebracan provide convergence of quotients in the quantum Gromov-Hausdorffpropinquity building off previous joint work with Latremoliere. These findingsbestow a continuous map from a class of ideals of the Boca-Mundici AF algebraequipped with various topologies including Jacobson and Fell topologies to thespace of quotients equipped with the propinquity topology.

Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals