Generalization of contra-continuous functions.
Generalizations of analytic and standard measurable spaces.
Generalized analytic spaces, completeness and fragmentability
Classical analytic spaces can be characterized as projections of Polish spaces. We prove analogous results for three classes of generalized analytic spaces that were introduced by Z. Frolík, D. Fremlin and R. Hansell. We use the technique of complete sequences of covers. We explain also some relations of analyticity to certain fragmentability properties of topological spaces endowed with an additional metric.
Generalized Lusin sets with the Blackwell property
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.
Generalized Radon spaces which are not Radon.
Generalized Sierpinski sets.
Generic power series on subsets of the unit disk
We examine the boundary behaviour of the generic power series with coefficients chosen from a fixed bounded set in the sense of Baire category. Notably, we prove that for any open subset of the unit disk with a nonreal boundary point on the unit circle, is a dense set of . As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given....