Perturbations of isometries between $C(K)$-spaces
Volume 166 / 2005
Studia Mathematica 166 (2005), 181-197
MSC: 46T99, 46E15, 46B26.
DOI: 10.4064/sm166-2-4
Abstract
We study the Gromov–Hausdorff and Kadets distances between $C(K)$-spaces and their quotients. We prove that if the Gromov–Hausdorff distance between $C(K)$ and $C(L)$ is less than $1/16$ then $K$ and $L$ are homeomorphic. If the Kadets distance is less than one, and $K$ and $L$ are metrizable, then $C(K)$ and $C(L)$ are linearly isomorphic. For $K$ and $L$ countable, if $C(L)$ has a subquotient which is close enough to $C(K)$ in the Gromov–Hausdorff sense then $K$ is homeomorphic to a clopen subset of $L.$
