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Uniform Algebras in the Cantor and Baire Spaces
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A. Nowik
Published/Copyright:
June 9, 2010
Abstract
For each pointclass Γ ⊆ P(2ω) define U[Γ] as the collection of all X ⊆ 2ω such that the preimage ƒ–1(X) belongs to Γ for each continuous ƒ : 2ω → 2ω. We study the properties of and possible relationships among the classes U[Γ], where Γ ranges over the σ-algebras (l), (m), the completely Ramsey sets, and the sets with the Baire property. We also prove some results about cardinal coefficients of U[Γ] for the general case of Marczewski-Burstin representable σ-algebras Γ. We finish by posing some unsolved problems.
Key words and phrases.: Ramsey set; Laver tree; superperfect tree; tree forcing; Marczewski-Burstin representation
Received: 2007-06-20
Revised: 2008-03-23
Published Online: 2010-06-09
Published in Print: 2008-December
© Heldermann Verlag
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Keywords for this article
Ramsey set;
Laver tree;
superperfect tree;
tree forcing;
Marczewski-Burstin representation
Articles in the same Issue
- Functions Preserving Some Types of Series
- On the Lipschitz Continuity of the Solutions of a Class of Elliptic Free Boundary Problems
- Distortion and Convolutional Theorems for Operators of Generalized Fractional Calculus Involving Wright Function
- Some New Generalizations of Critical Point Theorems for Locally Lipschitz Functions
- Stability of Impulsive Hybrid Set-Valued Differential Equations with Delay by Perturbing Lyapunov Functions
- Existence of Pareto Equilibria for Non-Compact Constrained Multi-Criteria Games
- Uniform Algebras in the Cantor and Baire Spaces
- Bounded Controllers for Uncertain Nonlinear Systems
- On a Refinement Type Equation
- Differential Polynomials Generated by Second Order Linear Differential Equations
- Existence Results of l-Point BVP for Higher Order Differential Equations with One-Dimension p-Laplacian
- Erratum to the Paper “Sufficiency and Duality in Control Problems with Generalized Invexity”
