On one generalization of the weakly compactly generated B-spaces
On pointwise limits of sequences of -continuous functions
On projection of nonseparable Souslin and Borel sets along separable spaces
On qualitative cluster sets
On sectorial qualitative cluster sets and directional qualitative cluster sets
On separation properties for families of probability measures.
On sequences of σ-algebras
On sets with Baire property in topological spaces
Steinhaus [9] prove that if a set has a positive Lebesgue measure in the line then its distance set contains an interval. He obtained even stronger forms of this result in [9], which are concerned with mutual distances between points in an infinite sequence of sets. Similar theorems in the case we replace distance by mutual ratio were established by Bose-Majumdar [1]. In the present paper, we endeavour to obtain some results related to sets with Baire property in locally compact topological spaces,...
On several classes of sets II.
On Sierpiński's nonmeasurable set
On similarity between topologies
Let T 1 and T 2 be topologies defined on the same set X and let us say that (X, T 1) and (X, T 2) are similar if the families of sets which have nonempty interior with respect to T 1 and T 2 coincide. The aim of the paper is to study how similar topologies are related with each other.
On small sets in the sense of measure and category
On some ideals and related algebras of sets in the plane
On some problem of A. Rosłanowski
We present a negative answer to problem 3.7(b) posed on page 193 of [2], where, in fact, A. Rosłanowski asked: Does every set of Lebesgue measure zero belong to some Mycielski ideal?
On some properties of Hurewicz, Menger, and Rothberger
On some properties of sets with positive measure
On some properties of the Cantor set
On s-sets in spaces of homogeneous type
Let (X,d,μ) be a space of homogeneous type. We study the relationship between two types of s-sets: relative to a distance and relative to a measure. We find a condition on a closed subset F of X under which F is an s-set relative to the measure μ if and only if F is an s-set relative to δ. Here δ denotes the quasi-distance defined by Macías and Segovia such that (X,δ,μ) is a normal space. In order to prove this result, we prove a covering type lemma and a type of Hausdorff measure based criterion...
On symmetric derivatives and on properties of Zahorski
On systems of null sets
The collection of all sets of measure zero for a finitely additive, group-valued measure is studied and characterised from a combinatorial viewpoint.