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Perturbations of isometries between C(K)-spaces

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Dutrieux Y., Kalton N.

Studia Mathematica

2005

tom 166

nr 2

181-197

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.

Ograniczanie wyników

1 Studia Mathematica

1 Dutrieux Y.

1 Kalton N.

1 2005

Wyniki wyszukiwania

Perturbations of isometries between C(K)-spaces