Lattices and Their Continuum Limits
نویسندگان
چکیده
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 C(M) of continuous functions onM . In a companion paper we shall extend this analysis to systems of noncommutative lattices (non Hausdorff lattices). ∗Address after September 1 : Departamento de Fisica Teorica, Facultade de Ciencias, Universitad de Zaragoza, 50009 Zaragoza, Spain.
منابع مشابه
The Erwin Schrr Odinger International Institute for Mathematical Physics Noncommutative Lattices and Their Continuum Limits Noncommutative Lattices and Their Continuum Limits
We consider nite 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 C(M) of continuous functions on M. We show how to recover the space M and the algebra C(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C-algebras, re...
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