Perturbations of isometries between C(K)-spaces

Yves Dutrieux, and Nigel J. Kalton. "Perturbations of isometries between C(K)-spaces." Studia Mathematica 166.2 (2005): 181-197. <http://eudml.org/doc/284708>.

@article{YvesDutrieux2005,
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.},
author = {Yves Dutrieux, Nigel J. Kalton},
journal = {Studia Mathematica},
keywords = {Hausdorff distance; Gromov–Hausdorff distance; Kadets distance; -spaces; Szlenk index},
language = {eng},
number = {2},
pages = {181-197},
title = {Perturbations of isometries between C(K)-spaces},
url = {http://eudml.org/doc/284708},
volume = {166},
year = {2005},
}

TY - JOUR
AU - Yves Dutrieux
AU - Nigel J. Kalton
TI - Perturbations of isometries between C(K)-spaces
JO - Studia Mathematica
PY - 2005
VL - 166
IS - 2
SP - 181
EP - 197
AB - 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.
LA - eng
KW - Hausdorff distance; Gromov–Hausdorff distance; Kadets distance; -spaces; Szlenk index
UR - http://eudml.org/doc/284708
ER -