Abstract:We study topological aspects of the category of abstract Cuntz semigroups, termed Cu. We provide a suitable setting in which we are able to uniformly control how to approach an element of a Cusemigroup by a rapidly increasing sequence. This approximation induces a semimetric on the set of Cumorphisms, generalizing Cu-metrics that had been constructed in the past for some particular cases. Further, we develop an approximate intertwining theory for the category Cu. Finally, we give several applications such as t… Show more
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