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- W4382319341 abstract "For separable $C^*$-algebras $A$ and $B$, we define a topology on the set $[[A, B]]$ consisting of homotopy classes of asymptotic morphisms from $A$ to $B$. 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 $E$-theory group $E(A, B)$ with properties analogous to those of the topology on $KK(A, B)$. The Hausdorffized $E$-theory group $EL(A, B) = E(A, B) / overline{{0}}$ is also introduced and studied. We obtain a continuity result for the functor $EL(,cdot,,B)$, which implies a new continuity result for the functor $KL(,cdot,,B)$." @default.
- W4382319341 created "2023-06-28" @default.
- W4382319341 creator A5066434372 @default.
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- W4382319341 date "2023-06-23" @default.
- W4382319341 modified "2023-09-25" @default.
- W4382319341 title "A topology on E-theory" @default.
- W4382319341 doi "https://doi.org/10.48550/arxiv.2306.13757" @default.
- W4382319341 hasPublicationYear "2023" @default.
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