30 citations · 63 across the 24 of their papers we have counts for
7 papers · 2 filters
Inductive topological Hausdorff dimensions and fibers of generic continuous functions
Richárd Balka
In an earlier paper Buczolich, Elekes and the author introduced a new concept of dimension for metric spaces, the so called topological Hausdorff dimension. They proved that it is…
Answer to a question of Kolmogorov
Richárd Balka, Márton Elekes, András Máthé
More than 80 years ago Kolmogorov asked the following question. Let be a measurable set with , where denotes the two-dimensional…
Dimension and measure for generic continuous images
Richárd Balka, Ábel Farkas, Jonathan M. Fraser +1
We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, , into . The key question is `what is the gener…
Generalized Hausdorff measure for generic compact sets
Richárd Balka, András Máthé
Let be a Polish space. We prove that the generic compact set (in the sense of Baire category) is either finite or there is a continuous gauge function such t…
Duality between measure and category in uncountable locally compact abelian Polish groups
Richárd Balka
We show that there is no addition preserving Erdős-Sierpiński mapping on any uncountable locally compact abelian Polish group. This generalizes results of Bartoszyński and Kysiak.
Intersection of continua and rectifiable curves
Richárd Balka, Viktor Harangi
We prove that for any non-degenerate continuum there exists a rectifiable curve such that its intersection with has Hausdorff dimension 1. This answe…
Metric spaces admitting only trivial weak contractions
Richárd Balka
If is a metric space then the map is defined to be a weak contraction if for all , . We determine the simplest non…