O riešení niektorých nerozhodnutelných topologických problémov
On a local form of Lobachevski's functional equation
On a perfect set
On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents
On a question of H. Kraljevic.
On a question of Sierpiński
There is a set U of reals such that for every analytic set A there is a continuous function f which maps U bijectively to A.
On absolutely measurable sets
On absolutely operations
On Borel reducibility in generalized Baire space
We study the Borel reducibility of Borel equivalence relations on the generalized Baire space for an uncountable κ with . The theory looks quite different from its classical counterpart where κ = ω, although some basic theorems do generalize.
On completely Ramsey sets
On complexity of a set of norms in Banach spaces
On concentrated sets and N-sets
On countable cofinality and decomposition of definable thin orderings
We prove that in some cases definable thin sets (including chains) of Borel partial orderings are necessarily countably cofinal. This includes the following cases: analytic thin sets, ROD thin sets in the Solovay model, and Σ¹₂ thin sets under the assumption that for all reals x. We also prove that definable thin wellorderings admit partitions into definable chains in the Solovay model.
On families of σ-complete ideals
On game ideals
On ideals with projective bases.
On idempotent filters
On invariants for measure preserving transformations
The classification problem for measure preserving transformations is strictly more complicated than that of graph isomorphism.
On Marczewski sets and some ideals.
On Meager Additive and Null Additive Sets in the Cantor Space and in ℝ
Let T be the standard Cantor-Lebesgue function that maps the Cantor space onto the unit interval ⟨0,1⟩. We prove within ZFC that for every , X is meager additive in iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in and ℝ.