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Given a unital AF-algebra $A$ equipped with a faithful tracial state, weequip each (norm-closed two-sided) ideal of $A$ with a metrized quantum vectorbundle structure, when canonically viewed as a module over $A$, in the sense ofLatr\'emoli\`ere using previous work of the first author and Latr\'emoli\`ere.Moreover, we show that convergence of ideals in the Fell topology impliesconvergence of the associated metrized quantum vector bundles in the modularGromov-Hausdorff propinquity of Latr\'emoli\`ere. In a similar vein butrequiring a different approach, given a compact metric space $(X,d)$, we equipeach ideal of $C(X)$ with a metrized quantum vector bundle structure, and showthat convergence in the Fell topology implies convergence in the modularGromov-Hausdorff propinquity.

The Fell topology and the modular Gromov-Hausdorff propinquity