5 citations · 7 across the 7 of their papers we have counts for
7 papers
Continuous colorings on compact spaces
Noé de Rancourt, Dominique Lecomte, Miroslav Zelen
We study several natural classes of graphs on a zero-dimensional metrizable compact space having no continuous coloring. We compare these graphs with the quasi-order associated wit…
There is no bound on Borel classes of the graphs in the Luzin-Novikov theorem
P. Holicky, M. Zeleny
We show that for every ordinal there is a closed set such that for every the section is a two-poin…
Analytic digraphs of uncountable Borel chromatic number under injective definable homomorphism
Dominique Lecomte, Miroslav Zeleny
We study the analytic digraphs of uncountable Borel chromatic number on Polish spaces, and compare them with the notion of injective Borel homomorphism. We provide some minimal dig…
Universal and complete sets in martingale theory
Dominique Lecomte, Miroslav Zeleny
The Doob convergence theorem implies that the set of divergence of any martingale has measure zero. We prove that, conversely, any subset of the Cantor space with Lebesgu…
Borel chromatic number of closed graphs
Dominique Lecomte, Miroslav Zeleny
We construct, for each countable ordinal , a closed graph with Borel chromatic number two and Baire class chromatic number .
On Separable Determination of Sigma-P-Porous Sets in Banach Spaces
Marek Cuth, Martin Rmoutil, Miroslav Zeleny
We use a method involving elementary submodels and a partial converse of Foran lemma to prove separable reduction theorems concerning Suslin sigma-P-porous sets where "P" can be fr…
Descriptive complexity of countable unions of Borel rectangles
Dominique Lecomte, Miroslav Zeleny
We give, for each countable ordinal , an example of a countable union of Borel rectangles that cannot be decomposed into countably many rectangle…