95-433 Bimonte G., Ercolessi E., Landi G., Lizzi F., Sparano G., Teotonio-Sobrinho P.

LATTICES AND THEIR CONTINUUM LIMITS (39K, LaTeX) Sep 28, 95

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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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