6 papers
On two consequences of CH established by Sierpinski. II
Roman Pol, Piotr Zakrzewski
We continue a study of the relations between two consequences of the Continuum Hypothesis discovered by Waclaw Sierpinski, concerning uniform continuity of continuous functions and…
On two consequences of CH established by Sierpiński
Roman Pol, Piotr Zakrzewski
We study the relations between two consequences of the Continuum Hypothesis discovered by Wacław Sierpiński, concerning uniform continuity of continuous functions and uniform conve…
Countably perfectly meager and countably perfectly null sets
Tomasz Weiss, Piotr Zakrzewski
We study a strengthening of the notion of a universally meager set and its dual counterpart that strengthens the notion of a universally null set. We say that a subset of a per…
Countably perfectly meager sets
Roman Pol, Piotr Zakrzewski
We study a strengthening of the notion of a perfectly meager set. We say that that a subset of a perfect Polish space is countably perfectly meager in , if for every seq…
On Mazurkiewicz's sets, thin σ-ideals of compact sets and the space of probability measures on the rationals
Roman Pol, Piotr Zakrzewski
We shall establish some properties of thin -ideals of compact sets in compact metric spaces (in particular, the -ideals of compact null-sets for thin subadditive capacities),…
On Borel maps, calibrated -ideals and homogeneity
Roman Pol, Piotr Zakrzewski
Let be a Borel measure on a compactum . The main objects in this paper are -ideals , , of Borel sets in that can be covered by countably many…