1988•Journal of the London Mathematical SocietyRequires access

Functions of the First Baire Class

Claude Ambrose Rogers

Abstract

Let f be a function of the first Borel class mapping the metric space X to the metric space Y: Hansell has claimed that, if f is σ-discrete and Y has the extension property for X, then f is necessarily of the first Baire class; but his proof is incomplete. It is shown that the result is true if Y also has a certain local extension property for X. Conditions are given that ensure that Y has both extension properties for X.

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Key concepts: Baire measure, Extension (predicate logic), Baire space, Baire category theorem, Class (philosophy), Mathematics, Complete metric space, Property (philosophy)