30 citations · 63 across the 24 of their papers we have counts for
5 papers · 2 filters
The structure of continuous rigid functions of two variables
Richárd Balka, Márton Elekes
A function $f:\RR^n \to \RR$ is called \emph{vertically rigid} if is isometric to for all . We settled Janković's conjecture in a separate paper b…
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…
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…