Memoirs of the American Mathematical Society 2004; 91 pp; softcover Volume: 168 ISBN10: 0821835181 ISBN13: 9780821835180 List Price: US$63 Individual Members: US$37.80 Institutional Members: US$50.40 Order Code: MEMO/168/796
 By a quantum metric space we mean a \(C^*\)algebra (or more generally an orderunit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of GromovHausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, \(A_\theta\). We show, for consistently defined "metrics", that if a sequence \(\{\theta_n\}\) of parameters converges to a parameter \(\theta\), then the sequence \(\{A_{\theta_n}\}\) of quantum tori converges in quantum GromovHausdorff distance to \(A_\theta\). Readership Graduate students and research mathematicians interested in functional analysis. Table of Contents  GromovHausdorff distance for quantum metric spaces
 Bibliography
 Matrix algebras Converge to the sphere for quantum GromovHausdorff distance
 Bibliography
