Noncommutative Lattices and Their Continuum Limits
arXiv:hep-th/9507148 · doi:10.1016/S0393-0440(95)00064-X
Abstract
We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions on $M$. We show how to recover the space $M$ and the algebra $\cc(M)$ from a projective system of noncommutative lattices and an inductive system of noncommutative $C^*$-algebras, respectively.
22 pages, 8 Figures included in the LaTeX Source New version, minor modifications (typos corrected) and a correction in the list of authors