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arXiv · hep-th/9507147

Lattices and Their Continuum Limits

G. Bimonte·E. Ercolessi·G. Landi·F. Lizzi·G. Sparano·P. Teotonio-Sobrinho
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Abstract

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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G. Bimonte, E. Ercolessi, G. Landi, F. Lizzi, G. Sparano, P. Teotonio-Sobrinho. 1995-09-28. Lattices and Their Continuum Limits. https://doi.org/10.1016/s0393-0440(95)00063-1

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