Displaying similar documents to “Two counterexamples concerning Hausdorff dimensions of projections”

Separation conditions on controlled Moran constructions

Antti Käenmäki, Markku Vilppolainen (2008)

Fundamenta Mathematicae

Similarity:

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.

Non-subharmonicity of the Hausdorff distance

Edoardo Vesentini (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.

On the Hausdorff dimension of a family of self-similar sets with complicated overlaps

Balázs Bárány (2009)

Fundamenta Mathematicae

Similarity:

We investigate the properties of the Hausdorff dimension of the attractor of the iterated function system (IFS) {γx,λx,λx+1}. Since two maps have the same fixed point, there are very complicated overlaps, and it is not possible to directly apply known techniques. We give a formula for the Hausdorff dimension of the attractor for Lebesgue almost all parameters (γ,λ), γ < λ. This result only holds for almost all parameters: we find a dense set of parameters (γ,λ) for which the Hausdorff...

Contracting-on-Average Baker Maps

Michał Rams (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

We estimate from above and below the Hausdorff dimension of SRB measure for contracting-on-average baker maps.

Hausdorff gaps and towers in 𝓟(ω)/Fin

Piotr Borodulin-Nadzieja, David Chodounský (2015)

Fundamenta Mathematicae

Similarity:

We define and study two classes of uncountable ⊆*-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. We also indicate possible ways of developing a structure theory for towers based on classification of their Tukey types.

Perturbations of isometries between C(K)-spaces

Yves Dutrieux, Nigel J. Kalton (2005)

Studia Mathematica

Similarity:

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. ...

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

Ondřej Zindulka (2012)

Fundamenta Mathematicae

Similarity:

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.

Covering the real line with translates of a zero-dimensional compact set

András Máthé (2011)

Fundamenta Mathematicae

Similarity:

We construct a compact set C of Hausdorff dimension zero such that cof(𝒩) many translates of C cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.