On Borel Mappings and Baire Functions

DOI10.2307/1996801zbMath0295.54047OpenAlexW4233530961MaRDI QIDQ4048242

Roger W. Hansell

Publication date: 1974

Full work available at URL: https://doi.org/10.2307/1996801

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Special maps on topological spaces (open, closed, perfect, etc.) (54C10) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05) Classification of real functions; Baire classification of sets and functions (26A21)

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An Axiom for Nonseparable Borel Theory ⋮ First class selectors for upper semi-continuous multifunctions ⋮ Borel selectors for upper semi‐continuous multi‐valued functions ⋮ Extending Baire-one functions on compact spaces ⋮ A Counterexample to the Generalized Banach Theorem ⋮ Each weakly countably determined Asplund space admits a Fréchet differentiable norm ⋮ Some observations on `A new proof of a theorem of Jayne and Rogers' ⋮ Invariance of Borel classes in metric spaces ⋮ Extension of Borel maps with values in non-metrizable spaces ⋮ Absolute Souslin-\({\mathcal F}\) spaces and other weak-invariants of the norm topology ⋮ Compactness in function spaces ⋮ K ‐analytic sets ⋮ Descriptive classes of sets in nonseparable spaces ⋮ The first homotopic Baire class of maps with values in ANR's coincides with the first Baire class ⋮ EXTENSION OF CONTINUOUS MAPPINGS AND H₁-RETRACTS ⋮ On composition of Baire functions ⋮ There are \(2^{\mathfrak{c}}\) quasicontinuous non Borel functions on uncountable Polish space ⋮ Borel isomorphisms at the first level—I ⋮ Upper semi-continuous set-valued functions ⋮ Functionally \(\sigma\)-discrete mappings and a generalization of Banach's theorem ⋮ Correction to: Upper semi-continuous set-valued functions ⋮ Analytic and Luzin spaces (non-separable case) ⋮ Borel selectors for upper semi-continuous multi-valued functions ⋮ On σ-discrete borel mappings via quasi-metrics ⋮ Borel selectors for upper semi-continuous set-valued maps

Cites Work

• Extension of functions on fully normal spaces
• Über analytisch darstellbare Operation in abstrakten Räumen
• Borel Measurable Mappings for Nonseparable Metric Spaces
• Metrization of Topological Spaces
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