All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 29

Showing per page

Can we assign the Borel hulls in a monotone way?

Márton Elekes, András Máthé (2009)

Fundamenta Mathematicae

A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ G δ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone G δ hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent....

Choquet simplexes whose set of extreme points is K -analytic

Michel Talagrand (1985)

Annales de l'institut Fourier

We construct a Choquet simplex K whose set of extreme points T is 𝒦 -analytic, but is not a 𝒦 -Borel set. The set T has the surprising property of being a K σ δ set in its Stone-Cech compactification. It is hence an example of a K σ δ set that is not absolute.

Classes de Wadge potentielles et théorèmes d'uniformisation partielle

Dominique Lecomte (1993)

Fundamenta Mathematicae

On cherche à donner une construction aussi simple que possible d'un borélien donné d'un produit de deux espaces polonais. D'où l'introduction de la notion de classe de Wadge potentielle. On étudie notamment ce que signifie "ne pas être potentiellement fermé", en montrant des résultats de type Hurewicz. Ceci nous amène naturellement à des théorèmes d'uniformisation partielle, sur des parties "grosses", au sens du cardinal ou de la catégorie.

Combinatorics of ideals --- selectivity versus density

A. Kwela, P. Zakrzewski (2017)

Commentationes Mathematicae Universitatis Carolinae

This note is devoted to combinatorial properties of ideals on the set of natural numbers. By a result of Mathias, two such properties, selectivity and density, in the case of definable ideals, exclude each other. The purpose of this note is to measure the ``distance'' between them with the help of ultrafilter topologies of Louveau.

Compact covering mappings and cofinal families of compact subsets of a Borel set

G. Debs, J. Saint Raymond (2001)

Fundamenta Mathematicae

Among other results we prove that the topological statement “Any compact covering mapping between two Π⁰₃ spaces is inductively perfect” is equivalent to the set-theoretical statement " ∀ α ∈ ω ω , ω ₁ L ( α ) < ω ₁ "; and that the statement “Any compact covering mapping between two coanalytic spaces is inductively perfect” is equivalent to “Analytic Determinacy”. We also prove that these statements are connected to some regularity properties of coanalytic cofinal sets in (X), the hyperspace of all compact subsets of a Borel...

Compactifications of ℕ and Polishable subgroups of S ∞

Todor Tsankov (2006)

Fundamenta Mathematicae

We study homeomorphism groups of metrizable compactifications of ℕ. All of those groups can be represented as almost zero-dimensional Polishable subgroups of the group S ∞ . As a corollary, we show that all Polish groups are continuous homomorphic images of almost zero-dimensional Polishable subgroups of S ∞ . We prove a sufficient condition for these groups to be one-dimensional and also study their descriptive complexity. In the last section we associate with every Polishable ideal on ℕ a certain Polishable...

Complete pairs of coanalytic sets

Jean Saint Raymond (2007)

Fundamenta Mathematicae

Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of ω ω there exists a continuous function f : ω ω → X such that f - 1 ( C ₀ ) = D ₀ and f - 1 ( C ₁ ) = D ₁ . We give several explicit examples of complete pairs of coanalytic sets.

Complexité des boréliens à coupes dénombrables

Dominique Lecomte (2000)

Fundamenta Mathematicae

Nous donnons, pour chaque niveau de complexité Γ, une caractérisation du type "test d'Hurewicz" des boréliens d'un produit de deux espaces polonais ayant toutes leurs coupes dénombrables ne pouvant pas être rendus Γ par changement des deux topologies polonaises.

Complexity of curves

Udayan B. Darji, Alberto Marcone (2004)

Fundamenta Mathematicae

We show that each of the classes of hereditarily locally connected, finitely Suslinian, and Suslinian continua is Π₁¹-complete, while the class of regular continua is Π₀⁴-complete.

Complexity of the class of Peano functions

K. Omiljanowski, S. Solecki, J. Zielinski (2000)

Colloquium Mathematicae

We evaluate the descriptive set theoretic complexity of the space of continuous surjections from ℝ m to ℝ n .

Currently displaying 1 – 20 of 29

Page 1 Next