857 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Hungarian Academy of SciencesHU402 papers
- Eötvös Loránd UniversityHU156 papers
- Budapest University of Technology and EconomicsHU58 papers
- Central European UniversityAT42 papers
- École Polytechnique Fédérale de LausanneCH31 papers
- Central European University - Budapest Campus24 papers
- University of PannoniaHU23 papers
- Centre National de la Recherche ScientifiqueFR21 papers
- University College LondonGB20 papers
- University of SzegedHU20 papers
- University of Illinois Urbana-ChampaignUS18 papers
- Charles UniversityCZ15 papers
11 papers · 2 filters
Hausdorff measures of different dimensions are isomorphic under the Continuum Hypothesis
Márton Elekes
We show that the Continuum Hypothesis implies that for every the measure spaces $(\RR^n,\iM_{\iH^{d_1}},\iH^{d_1})$ and $(\RR^n,\iM_{\iH^{d_2}},\iH^{d_2})$ are is…
Borel sets which are null or non--finite for every translation invariant measure
Márton Elekes, Tamás Keleti
We show that the set of Liouville numbers is either null or non--finite with respect to every translation invariant Borel measure on $\RR$, in particular, with respect to every…
The structure of rigid functions
Richárd Balka, Márton Elekes
A function $f:\RR \to \RR$ is called \emph{vertically rigid} if is isometric to for all . We prove Janković's conjecture by showing that a continu…
Continuous horizontally rigid functions of two variables are affine
Richárd Balka, Márton Elekes
Cain, Clark and Rose defined a function $f\colon \RR^n \to \RR$ to be \emph{vertically rigid} if $\graph(cf)$ is isometric to $\graph (f)$ for every . It is \emph{horizon…
A cardinal number connected to the solvability of systems of difference equations in a given function class
Márton Elekes, Miklós Laczkovich
Let denote the set of real valued functions defined on the real line. A map is a {\it difference operator}, if there are real numbers $a_i, b_i \ (i=1,…
Can we assign the Borel hulls in a monotone way?
Márton Elekes, András Máthé
A \emph{hull} of is a set containing such that . We investigate all four versions of the following problem. Does there exist a monotone (wr…
Reconstructing geometric objects from the measures of their intersections with test sets
Márton Elekes, Tamás Keleti, András Máthé
Let us say that an element of a given family $\A$ of subsets of can be reconstructed using test sets if there exist such that whenever $A,B\in…
On a converse to Banach's Fixed Point Theorem
Márton Elekes
We say that a metric space possesses the \emph{Banach Fixed Point Property (BFPP)} if every contraction has a fixed point. The Banach Fixed Point Theorem says th…
Topological Hausdorff dimension and level sets of generic continuous functions on fractals
Richard Balka, Zoltan Buczolich, Marton Elekes
In an earlier paper (arxiv:1108.4292) we introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. For a compact metric space let…
A new fractal dimension: The topological Hausdorff dimension
Richárd Balka, Zoltán Buczolich, Márton Elekes
We introduce a new concept of dimension for metric spaces, the so-called topological Hausdorff dimension. It is defined by a very natural combination of the definitions of the topo…
How large dimension guarantees a given angle?
Viktor Harangi, Tamás Keleti, Gergely Kiss +4
We study the following two problems: (1) Given and $\al$, how large Hausdorff dimension can a compact set $A\su\Rn$ have if does not contain three points that form an…