{"product_id":"9780821835180","title":"Gromov-Hausdorff Distance for Quantum Metric Spaces\/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance","description":"\u003cp\u003eBy a quantum metric space we mean a $C^*$-algebra (or more generally an order-unit 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 Gromov-Hausdorff distance. We show that the basic theorems of the classical theory have natural quantum analogues. Our main example involves the quantum tori, $A\\theta$. We show, for consistently defined 'metrics', that if a sequence $\\{\\thetan\\}$ of parameters converges to a parameter $\\theta$, then the sequence $\\{A{\\thetan}\\}$ of quantum tori converges in quantum Gromov-Hausdorff distance to $A\\theta$.\u003c\/p\u003e","brand":"Exclusive Books Online","offers":[{"title":"Default Title","offer_id":52684773851454,"sku":"9780821835180","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/files\/9780821835180.jpg?v=1764858475","url":"https:\/\/exclusivebooks.co.za\/products\/9780821835180","provider":"Exclusive Books Online","version":"1.0","type":"link"}