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.
Tests à la Hurewicz dans le plan
Nous donnons, pour une certaine catégorie de boréliens d'un produit de deux espaces polonais, comprenant les boréliens à coupes dénombrables, une caractérisation du type "test d'Hurewicz" de ceux ne pouvant pas être rendus différence transfinie d'ouverts par changement des deux topologies polonaises.
The Borel structure of the collections of sub-self-similar sets and super-self-similar sets.
The coarsest topology for -approximately continuous functions
The complexity of the set of squares in the homeomorphism group of the circle
The set of squares in the group of autohomeomorphisms of the circle is complete analytic, and hence analytic but not Borel.
The complexity of -discretely decomposable families in uniform spaces
The covering property for σ-ideals of compact, sets
The covering property for σ-ideals of compact sets is an abstract version of the classical perfect set theorem for analytic sets. We will study its consequences using as a paradigm the σ-ideal of countable closed subsets of .
The dimension of analytic sets
The fixed point set of open mappings on extremally disconnected spaces
We give an example of an extremally disconnected compact Hausdorff space with an open continuous selfmap such that the fixed point set is nonvoid and nowhere dense, respṫhat there is exactly one nonisolated fixed point.
The -topology and K-analytic spaces without perfect compact sets
The generic isometry and measure preserving homeomorphism are conjugate to their powers
It is known that there is a comeagre set of mutually conjugate measure preserving homeomorphisms of Cantor space equipped with the coinflipping probability measure, i.e., Haar measure. We show that the generic measure preserving homeomorphism is moreover conjugate to all of its powers. It follows that the generic measure preserving homeomorphism extends to an action of (ℚ, +) by measure preserving homeomorphisms, and, in fact, to an action of the locally compact ring 𝔄 of finite adèles. ...
The Ramsey sets and related sigma algebras and ideals
The structure of the -ideal of -porous sets
We show a general method of construction of non--porous sets in complete metric spaces. This method enables us to answer several open questions. We prove that each non--porous Suslin subset of a topologically complete metric space contains a non--porous closed subset. We show also a sufficient condition, which gives that a certain system of compact sets contains a non--porous element. Namely, if we denote the space of all compact subsets of a compact metric space with the Vietoris topology...
The Subset P+ And P- Of The Split Interval
The subsets P+ and P- of the split interval.