Displaying similar documents to “Onto Gelfand maps : appendix”

Perturbations of isometries between C(K)-spaces

Yves Dutrieux, Nigel J. Kalton (2005)

Studia Mathematica

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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. ...

Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

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It is well known that the open set condition and the positivity of the t-dimensional Hausdorff measure are equivalent on self-similar sets, where t is the zero of the topological pressure. We prove an analogous result for a class of Moran constructions and we study different kinds of Moran constructions in this respect.

Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps

Ondřej Zindulka (2012)

Fundamenta Mathematicae

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We prove that each analytic set in ℝⁿ contains a universally null set of the same Hausdorff dimension and that each metric space contains a universally null set of Hausdorff dimension no less than the topological dimension of the space. Similar results also hold for universally meager sets. An essential part of the construction involves an analysis of Lipschitz-like mappings of separable metric spaces onto Cantor cubes and self-similar sets.