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1

Effective decomposition of σ-continuous Borel functions

100%

Debs G.

Fundamenta Mathematicae

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2014

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tom 224

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nr 2

187-202

EN

We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering $(Aₙ)_{n∈ω}$ of X such that $f_{|Aₙ}$ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.

2

Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$

63%

Debs G., Raymond J. S.

Fundamenta Mathematicae

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1999

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tom 159

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nr 2

161-193

EN

We study properties of $∑^1_1$ and $π^1_1$ subsets of $ω^ω$ that are cofinal relative to the orders ≤ (≤*) of full (eventual) domination. We apply these results to prove that the topological statement "Any compact covering mapping from a Borel space onto a Polish space is inductively perfect" is equivalent to the statement "$∀α ∈ω^ω, ω^ω ∩ L(α )$ is bounded for ≤*".

3

Filter descriptive classes of Borel functions

63%

Debs G., Saint Raymond J.

Fundamenta Mathematicae

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2009

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tom 204

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nr 3

189-213

EN

We first prove that given any analytic filter ℱ on ω the set of all functions f on $2^{ω}$ which can be represented as the pointwise limit relative to ℱ of some sequence $(fₙ)_{n∈ω}$ of continuous functions ($f = lim_{ℱ} fₙ$), is exactly the set of all Borel functions of class ξ for some countable ordinal ξ that we call the rank of ℱ. We discuss several structural properties of this rank. For example, we prove that any free Π⁰₄ filter is of rank 1.

4

Stratégies gagnantes dans certains jeux topologiques

38%

Debs G.

Fundamenta Mathematicae

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1985-1986

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tom 126

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nr 1

93-105

Ograniczanie wyników

4 Fundamenta Mathematicae

4 Debs G.

1 Raymond J. S.

1 Saint Raymond J.

1 2014

1 2009

1 1999

1 1985

Effective decomposition of σ-continuous Borel functions

Cofinal $Σ^1_1$ and $Π^1_1$ subsets of $ω^ω$

Filter descriptive classes of Borel functions

Stratégies gagnantes dans certains jeux topologiques