Compact Quantum Metric Spaces

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We give a brief survey of many of the high-lights of our present understanding of the young subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between them. We include examples.
Intended for the proceedings of the AMS Special Session ``Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration in Honor of J. V. Neumann and M. H. Stone, II'', editors R. S. Doran and R. V. Kadison

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