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Wiley
Date
5/17/2024
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For separable -algebras and , we define a topology on the set [[,]] consisting of homotopy classes of asymptotic morphisms from to . This gives an enrichment of the Connes-Higson asymptotic category over topological spaces. We show that the Hausdorffization of this category is equivalent to the shape category of Dadarlat. As an application, we obtain a topology on the -theory group (,) with properties analogous to those of the topology on (,). The Hausdorffized -theory group (,) = (,)/{0} is also introduced and studied. We obtain a continuity result for the functor (,), which implies a new continuity result for the functor (,).
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Mathematics