22 citations · 59 across the 20 of their papers we have counts for
11 papers · 1 filter
Sequence spaces of Baire-one functions and their porosity
Marek Balcerzak, Gertruda Ivanova
We consider several families of sequences of Baire-one self-maps of investigated by A. Alikhani-Koopaei. They form a chain of inclusions where each space is closed and nowh…
Linear relations modulo meager sets
Marek Balcerzak, Paolo Leonetti
We prove several topological zero-one laws. First, we show that, if a subset of a Banach space has the Baire property, then admits a somewhere dense set of vectors $x \…
Topological complexity of ideal limit points
Marek Balcerzak, Szymon Glab, Paolo Leonetti
Given an ideal on the nonnegative integers and a Polish space , let be the family of subsets such that is the set…
Point-set games and functions with the hereditary small oscillation property
Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca
Given a metric space , we consider certain families of functions having the hereditary oscillation property HSOP and the hereditary continuous restriction pro…
Properties of equi-Baire 1 and equi-Lebesgue families of functions
Marek Balcerzak, Lubica Hola, Dusan Holy
We study several properties of equi-Baire 1 families of functions between metric spaces. We consider the related equi-Lebesgue property for such families. We examine the behaviour…
Baire Category Lower Density Operators with Borel Values
Marek Balcerzak, Jacek Hejduk, Artur Wachowicz
We prove that the lower density operator associated with the Baire category density points in the real line has Borel values of class which is analogous to the measure…
Another characterization of meager ideals
Marek Balcerzak, Szymon Glab, Paolo Leonetti
We show that an ideal on the positive integers is meager if and only if there exists a bounded nonconvergent real sequence such that the set of subsequences [resp…
Games characterizing certain families of functions
Marek Balcerzak, Tomasz Natkaniec, Piotr Szuca
We obtain several game characterizations of Baire 1 functions between Polish spaces X, Y which extends the recent result of V. Kiss. Then we propose similar characterizations for e…
The Baire Category of Subsequences and Permutations which preserve Limit Points
Marek Balcerzak, Paolo Leonetti
Let be a meager ideal on . We show that if is a sequence with values in a separable metric space then the set of subsequences [resp. permutations] of…
Families of feebly continuous functions and their properties
Marek Balcerzak, Tomasz Natkaniec, Małgorzata Terepeta
Let . The notions of feebly continuity and very feebly continuity of at a point were considered by I. Lead…
A lower density operator for the Borel algebra
Marek Balcerzak, Szymon Głab
We prove that the existence of a Borel lower density operator (a Borel lifting) with respect to the -ideal of countable sets, for an uncountable Polish space, is equivalent to t…