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In this paper it is demonstrated that the Kasparov pairing is continuous with respect to the natural topology on the Kasparov groups, so that a KK-equivalence is an isomorphism of topological groups. In addition, we demonstrate that the groups have a natural pseudopolonais structure, and we prove that various KK-structural maps are continuous.


Geometry and Topology | Mathematics


This is the author’s final accepted manuscript version of a work, derived from arXiv [], and subsequently accepted for publication in the Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the Journal of Functional Analysis, 186(1) (2001) []

1991 Mathematics Subject Classification: Primary 19K35, 46L80, 47A66; Secondary 19K56, 47C15.