Lattices and Their Continuum Limits

Details Lattices and Their Continuum Limits Lattices and Their Continuum Limits

1995-07-27

arxiv.org/abs/hep-th/9507147v2

J.Geom.Phys. 20 (1996) 318-328

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 1 Figure included in the LaTeX Source New version, minor modifications (typos corrected) and a correction in the lis

Scientific paper

10.1016/S0393-0440(95)00063-1

We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space $M$. The correct framework is that of projective systems. The projective limit is a universal space from which $M$ can be recovered as a quotient. We dualize the construction to approximate the algebra ${\cal C}(M)$ of continuous functions on $M$. In a companion paper we shall extend this analysis to systems of noncommutative lattices (non Hausdorff lattices).

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