V'aclav Vlas'ak

activity

20152026

collaborators

5 papers

math.LO2026

A nonmicroscopic $G_{δ}$ set with only microscopic compact subsets

Martin Doležal, Václav Vlasák

We construct a nonmicroscopic $G_{δ}$ subset of the real line all of whose compact subsets are microscopic, answering a question of Zindulka and Nowakowski. We first obtain such a se…

math.CA2019

On $k$ -antichains in the unit $n$ -cube

Christos Pelekis, Václav Vlasák

A \emph{chain} in the unit $n$ -cube is a set $C \subset [0, 1]^{n}$ such that for every $x = (x_{1}, \dots, x_{n})$ and $y = (y_{1}, \dots, y_{n})$ in $C$ we either have $x_i\le y_…

math.CA2019

A continuous analogue of Erdős' $k$ -Sperner theorem

Themis Mitsis, Christos Pelekis, Václav Vlasák

A \emph{chain} in the unit $n$ -cube is a set $C \subset [0, 1]^{n}$ such that for every $x = (x_{1}, \dots, x_{n})$ and $y = (y_{1}, \dots, y_{n})$ in $C$ we either have $x_i\le y_…

math.GN2016

Haar meager sets, their hulls, and relationship to compact sets

Martin Doležal, Václav Vlasák

Let $G$ be an abelian Polish group. We show that there is a strongly Haar meager set in $G$ without any $F_{σ}$ Haar meager hull (and that this still remains true if we replace $F_{σ}$ …

math.GN2015

Haar meager sets revisited

Martin Doležal, Martin Rmoutil, Benjamin Vejnar +1

In the present article we investigate Darji's notion of Haar meager sets from several directions. We consider alternative definitions and show that some of them are equivalent to t…

A nonmicroscopic Gδ​ set with only microscopic compact subsets

On k-antichains in the unit n-cube

A continuous analogue of Erdős' k-Sperner theorem

Haar meager sets, their hulls, and relationship to compact sets

Haar meager sets revisited

A nonmicroscopic $G_{δ}$ set with only microscopic compact subsets

On $k$ -antichains in the unit $n$ -cube

A continuous analogue of Erdős' $k$ -Sperner theorem