The Hamming Distance and the Fell Topology on AF Algebras

Abstract

We introduce a new metric on the ideal space of an AF algebra that metrizes the Fell topology. The novelty of this metric lies in the use of a Hamming distance type metric in its construction. Furthermore, this metric captures more of the ideal structure of AF algebras in comparison to known metrics on the Fell topology of an AF algebra. We explicitly test this on the C*-algebra of complex-valued continuous functions on a quantized interval by comparing our new metric with the dual Hausdorff distance on the ideals of this C*-algebras induced by the Hausdorff distance on the closed subsets of the quantized interval.