4 papers · 1 filter
Signed null sequences and Hausdorff dimension
Richárd Balka, Kornélia Héra, Gergely Kiss
We investigate the convergence of signed null sequences of the form \[ \sum_{n=1}^\infty \varepsilon_n a_n, \quad \varepsilon_n \in \{-1,1\}, \] where tends to zero in $\ma…
New Hausdorff type dimensions and optimal bounds for bilipschitz invariant dimensions
Richárd Balka, Tamás Keleti
We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that…
Lipschitz images and dimensions
Richárd Balka, Tamás Keleti
We consider the question which compact metric spaces can be obtained as a Lipschitz image of the middle third Cantor set, or more generally, as a Lipschitz image of a subset of a g…
The range of dimensions of microsets
Richárd Balka, Márton Elekes, Viktor Kiss
We say that is a microset of the compact set if there exist sequences and such that conv…