Functions with fibres large on each nonvoid open set
On the generalized Zink classification
Orthogonal σ-ideals and almost disjoint families
Same Bernstein-type construction and its applications
On ϭ-ideals without maximal extension
Ideal Convergence of Sequences and Some of its Applications
Remarks on products of σ-ideals
On c-sets and products of ideals
Let X, Y be uncountable Polish spaces and let μ be a complete σ-finite Borel measure on X. Denote by K and L the families of all meager subsets of X and of all subsets of Y with μ measure zero, respectively. It is shown that the product of the ideals K and L restricted to C-sets of Selivanovskiĭ is σ-saturated, which extends Gavalec's results.
Generalized projections of Borel and analytic sets
For a σ-ideal I of sets in a Polish space X and for A ⊆ , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ for a wide class of -supported σ-ideals.
On isomorphisms between -ideals on
A generalization of the theorem of Mauldin
On some ideals and related algebras of sets in the plane
Classification of -ideals
On the generalized property
Some examples of true sets
Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true sets.
On multiplication in spaces of continuous functions
We introduce and examine the notion of dense weak openness. In particular we show that multiplication in C(X) is densely weakly open whenever X is an interval in ℝ.
Convergence theorems for the Birkhoff integral
We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence of functions from a measure space to a Banach space. In one result the equi-integrability of ’s is involved and we assume almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of to is assumed.
On pointwise limits of sequences of -continuous functions
Marczewski sets in the Hashimoto topologies for measure and category
Lipschitz differences and Lipschitz functions
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