Noncommutative Lattices and Their Continuum Limits
نویسندگان
چکیده
We consider finite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutativeC∗-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, respectively. ∗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...
متن کاملThe Erwin Schrr Odinger International Institute for Mathematical Physics Lattices and Their Continuum Limits Lattices and Their Continuum Limits
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 companio...
متن کاملLattices and Their Continuum Limits
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 compan...
متن کاملLattices and Their Continuum
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 companio...
متن کاملNoncommutative Lattices and the Algebras of Their Continuous Functions
Recently a new kind of approximation to continuum topological spaces has been introduced, the approximating spaces being partially ordered sets (posets) with a finite or at most a countable number of points. The partial order endows a poset with a nontrivial non-Hausdorff topology. Their ability to reproduce important topological information of the continuum has been the main motivation for the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1995