Pure mathematics

Discrete mathematics

Covariant transformation

Hausdorff space

Economics

Metric space

Mathematics

Injective metric space

Mathematical analysis

Operations management

Geometry

Equivalence of metrics

Hausdorff distance

Metric (unit)

Convex metric space

Metric map

Advances in Mathematics

We define a metric on the class of metric spectral triples, which is null exactly between unitarily equivalent spectral triples. This metric dominates the propinquity, and thus implies metric convergence of the quantum compact metric spaces induced by metric spectral triples. In the process of our construction, we also introduce the covariant modular propinquity, as a key component for the definition of the spectral propinquity.

The Gromov-Hausdorff propinquity for metric spectral triples