The Erwin Schrr Odinger International Institute for Mathematical Physics Lattices and Their Continuum Limits Lattices and Their Continuum Limits
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چکیده
We address the problem of the continuum limit for a system of Hausdorr 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 on M. In a companion paper we shall extend this analysis to systems of noncommutative lattices (non Hausdoo lattices).
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...
متن کاملThe Erwin Schrr Odinger International Institute for Mathematical Physics K{theory of Noncommutative Lattices K-theory of Noncommutative Lattices
Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutati...
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