A property of the Sorgenfrey line
A remark on a theorem of Solecki
S. Solecki proved that if is a system of closed subsets of a complete separable metric space , then each Suslin set which cannot be covered by countably many members of contains a set which cannot be covered by countably many members of . We show that the assumption of separability of cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the -ideal generated by is locally determined. Using Solecki’s arguments, our result can be used...
A remark on the uniformization in metric ѕpaces
A scenario for transferring high scores
A separation theorem and applications to Borel sets
A stabilization property and its applications in the theory of sections
A strong boundedness result for separable Rosenthal compacta
It is proved that the class of separable Rosenthal compacta on the Cantor set having a uniformly bounded dense sequence of continuous functions is strongly bounded.
A survey of separable descriptive theory of sets and spaces
A topology generated by eventually different functions
A -porous set need not be -bilaterally porous
A closed subset of the real line which is right porous but is not -left-porous is constructed.
Abelian pro-countable groups and orbit equivalence relations
We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups....
About an example of a Banach space not weaky K-analytic.
Abstract analytic and borelian sets
Adequate Compacta which are Gul’ko or Talagrand
2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We answer positively a question raised by S. Argyros: Given any coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko and not Talagrand. Further, given any Borel, non Fσ subset Σ′ of the irrationals, we construct, in c1(Σ′), an adequate compact which is Talagrand and not Eberlein.Supported by grants AV CR 101-90-03, and GA CR 201-01-1198
Almost lower semicontinuous multifunctions and the Souslin-graph theorem
Always of the first category sets
Always of the first category sets (II)
An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions
We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...
An analytic equivalence relation not arising from a Polish group action
Analytic Baire spaces
We generalize to the non-separable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a joint-continuity result for non-separable normed groups, previously known only in the separable context.