We consider finite 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 \cc(M) of continuous functions on M. We show how to recover the space M and the algebra \cc(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C ∗-algebras, respectively.
Noncommutative lattices and their continuum limits
SPARANO, Giovanni;
1996-01-01
Abstract
We consider finite 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 \cc(M) of continuous functions on M. We show how to recover the space M and the algebra \cc(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C ∗-algebras, respectively.File in questo prodotto:
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