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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Perturbations of isometries between $C(K)$-spaces

### Tom 166 / 2005

Studia Mathematica 166 (2005), 181-197 MSC: 46T99, 46E15, 46B26. DOI: 10.4064/sm166-2-4

#### Streszczenie

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 $L.$

#### Autorzy

• Yves DutrieuxLaboratoire de Mathématiques
UMR 6623
Université de Franche-Comté
25030 Besançon Cedex, France
e-mail
• Nigel J. KaltonDepartment of Mathematics
University of Missouri-Columbia
Columbia, MO 65211, U.S.A.
e-mail

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