%0 Journal Article
%T Gromov-Hausdorff Distance for Quantum Metric Spaces
%A Marc A. Rieffel
%J Mathematics
%D 2000
%I arXiv
%X By a quantum metric space we mean a C^*-algebra (or more generally an order-unit space) equipped with a generalization of the Lipschitz seminorm on functions which is defined by an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, $A_{\th}$. We show, for consistently defined ``metrics'', that if a sequence $\{\th_n\}$ of parameters converges to a parameter $\th$, then the sequence $\{A_{\th_n}\}$ of quantum tori converges in quantum Gromov-Hausdorff distance to $A_{\th}$.
%U http://arxiv.org/abs/math/0011063v4