Refinements of Lebesgue covers
Remark on completely Baire-additive families in analytic spaces
Remark on the Abstract Dirichlet Problem for Baire-One Functions
We study the possibility of extending any bounded Baire-one function on the set of extreme points of a compact convex set to an affine Baire-one function and related questions. We give complete solutions to these questions within a class of Choquet simplices introduced by P. J. Stacey (1979). In particular we get an example of a Choquet simplex such that its set of extreme points is not Borel but any bounded Baire-one function on the set of extreme points can be extended to an affine Baire-one function....
Remarks on a game of Choquet
Remarks on density topology and its category analogue
Remarks on -density and -approximately continuous functions
Selection theorems for partitions of Polish spaces
Selections using orderings (non-separable case)
Selivanovski hard sets are hard
Let . For n ≥ 2, we prove that if Selivanovski measurable functions from to Z give as preimages of H all Σₙ¹ subsets of , then so do continuous injections.
Semi-continuity of set-valued monotone mappings
Sets with no uncountable Blackwell subsets
Small sets with respect to certain classes of topologies
Solution of a G. Kurepa's problem
Solution of a problem of Ulam on countable sequences of sets
Some applications of game determinacy
Some comments on infinite Boolean functions
We introduce infinite Boolean functions and investigate some of their properties.
Some Comments on Q-Irresolute and Quasi-Irresolute Functions
The aim of this paper is to continue the study of θ-irresolute and quasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer to a question posed by Ganster, Noiri and Reilly. We prove that RS-compactness is preserved under open, quasi-irresolute surjections.
Some examples in the theory of Borel sets
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.
Some facts from descriptive set theory concerning essential spectra and applications
Let X be a separable Banach space and denote by 𝓛(X) (resp. 𝒦(ℂ)) the set of all bounded linear operators on X (resp. the set of all compact subsets of ℂ). We show that the maps from 𝓛(X) into 𝒦(ℂ) which assign to each element of 𝓛(X) its spectrum, approximate point spectrum, essential spectrum, Weyl essential spectrum, Browder essential spectrum, respectively, are Borel maps, where 𝓛(X) (resp. 𝒦(ℂ)) is endowed with the strong operator topology (resp. Hausdorff topology). This enables us...