Bimonte G., Ercolessi E., Landi G., Lizzi F., Sparano G., Teotonio-Sobrinho P.
NONCOMMUTATIVE LATTICES AND THEIR CONTINUUM LIMITS
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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.