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...
Some problems on Suslin spaces and topological algebras
Some remarks on Suslin sections
Some Results on Analytic Spaces and Semi-Analytic Functions with Regard to Gambling Theory.
Some uniformization results
Spaces of measurable functions
For a metrizable space X and a finite measure space (Ω, , µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of -measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.
Split Faces and Projective Sets in a Metrizable Compact Convex Set.