On a class of indecomposable continua
On a classification of pointwise compact sets of the first Baire class functions
On a Freedman's problem
On a game of Sierpiński
On a modified game of Sierpiński
On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents
On a theorem of Holický and Zelený concerning Borel maps without -compact fibers
The paper is concerned with a recent very interesting theorem obtained by Holický and Zelený. We provide an alternative proof avoiding games used by Holický and Zelený and give some generalizations to the case of set-valued mappings.
On a theorem of Popa and Noiri on multifunctions
On a universality property of some abelian Polish groups
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
On a weak form of uniform convergence
The notion of -convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on implies -convergence are -compact spaces. We show that the assumption...
On absolutely measurable sets
On absolutely operations
On an Abstract Formulation of Regularity
On analytic-dense Blackwell sets
On analyticity in cosmic spaces
We prove that a cosmic space (= a Tychonoff space with a countable network) is analytic if it is an image of a -analytic space under a measurable mapping. We also obtain characterizations of analyticity and -compactness in cosmic spaces in terms of metrizable continuous images. As an application, we show that if is a separable metrizable space and is its dense subspace then the space of restricted continuous functions is analytic iff it is a -space iff is -compact.
On Borel Classes of Sets of Fréchet Subdifferentiability
We study possible Borel classes of sets of Fréchet subdifferentiability of continuous functions on reflexive spaces.
On Borel measurability of orbits
On Borel-measurable collections of countable-dimensional sets
On clopen sets in Cartesian products
The results concern clopen sets in products of topological spaces. It is shown that a clopen subset of the product of two separable metrizable (or locally compact) spaces is not always a union of clopen boxes. It is also proved that any clopen subset of the product of two spaces, one of which is compact, can always be represented as a union of clopen boxes.
On cluster sets of arbitrary functions