Corrigendum: A topology on E $E$ -theory

Abstract

The second sentence of [1, Corollary 4.4] does not follow from the given reference, and we do not know if it is true as stated. What is true is that if $\overline{x}\in {\left[[A,B]\right]}_{\mathrm{Hd}}$ is an isomorphism, then there is an isomorphism $x\in \left[\right[A,B\left]\right]$ such that $\mathrm{Hd}\left(x\right)=\overline{x}$. Indeed, [2, Theorem 1.14] implies every isomorphism in the shape category $\mathrm{sh}$ is induced by an isomorphism in the strong shape category $s$-$\mathrm{sh}$, and then the result follows from using [1, Theorem 4.3; 2, Theorem 3.7] to identify these categories with the Hausdorffized asymptotic morphism category ${\mathrm{AM}}_{\mathrm{Hd}}$ and the asymptotic morphism category $\mathrm{AM}$.

This error has no effect on the rest of the results in the paper.