Decomposing Borel functions and structure at finite levels of the Baire hierarchy

DOI10.1016/j.apal.2012.03.004zbMath1259.03061arXiv0908.1544OpenAlexW2019997327MaRDI QIDQ714711

Marcin Sabok, Janusz Pawlikowski

Publication date: 11 October 2012

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.1544

zbMATH Keywords

analytic setscountably continuous functionsdecomposition of functions

Mathematics Subject Classification ID

Descriptive set theory (03E15) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items (13)

Luzin's topological problem ⋮ Descriptive complexity of \(\mathsf{qc} \mathsf{b}_0\)-spaces ⋮ Borel-Piecewise Continuous Reducibility for Uniformization Problems ⋮ Inside the Muchnik degrees. II: The degree structures induced by the arithmetical hierarchy of countably continuous functions ⋮ On Mazurkiewicz's sets, thin \(\sigma\)-ideals of compact sets and the space of probability measures on the rationals ⋮ Embeddability on functions: Order and chaos ⋮ Wadge-like reducibilities on arbitrary quasi-Polish spaces ⋮ \(\sigma\)-continuous functions and related cardinal characteristics of the continuum ⋮ Decomposing Borel functions using the Shore–Slaman join theorem ⋮ Turing degrees in Polish spaces and decomposability of Borel functions ⋮ DECOMPOSING FUNCTIONS OF BAIRE CLASS ON POLISH SPACES ⋮ Point Degree Spectra of Represented Spaces ⋮ On Ohta-Sakai's properties of a topological space

Cites Work

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• A new proof of a theorem of Jayne and Rogers
• First level Borel functions and isomorphisms
• Baire 1 functions which are not countable unions of continuous functions
• Game representations of classes of piecewise definable functions
• Countable Decomposition of Derivatives and Baire 1 Functions
• Some examples of Borel sets
• Universal Functions and Generalized Classes of Functions
• Decomposing Baire functions
• A very discontinuous Borel function
• Some complexity results in topology and analysis
• Decomposing Borel sets and functions and the structure of Baire class 1 functions
• Descriptive set theory and definable forcing
• Baire reductions and good Borel reducibilities
• Some examples of Borel sets

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