Geodesic
Perturbations of isometries between $C(K)$-spaces
Yves Dutrieux1 ; Nigel J. Kalton2
1 Laboratoire de Mathématiques UMR 6623 Université de Franche-Comté 25030 Besançon Cedex, France
2 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A.
Studia Mathematica, Tome 166 (2005) no. 2, pp. 181-197

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $L.$
DOI : 10.4064/sm166-2-4
Keywords: study gromov hausdorff kadets distances between spaces their quotients prove gromov hausdorff distance between homeomorphic kadets distance and metrizable linearly isomorphic countable has subquotient which close enough gromov hausdorff sense homeomorphic clopen subset

Yves Dutrieux 1 ; Nigel J. Kalton 2

1 Laboratoire de Mathématiques UMR 6623 Université de Franche-Comté 25030 Besançon Cedex, France
2 Department of Mathematics University of Missouri-Columbia Columbia, MO 65211, U.S.A. 
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Yves Dutrieux; Nigel J. Kalton. Perturbations of isometries between $C(K)$-spaces. Studia Mathematica, Tome 166 (2005) no. 2, pp. 181-197. doi: 10.4064/sm166-2-4

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