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Characterization of Baire-one functions between topological spaces. (English) Zbl 0792.54028

Summary: Let \(X\) be a normal topological space and \(Y\) be a metric space. We give several sufficient conditions under which the functions of the first Baire class from \(X\) into \(Y\) are characterized by their \(F_ \sigma\)- measurability and strong \(\sigma\)-discreteness. For example, this happens if \(Y\) is arcwise connected and locally arcwise connected, or if \(Y\) contains a dense subspace \(Y_ 1\) such that all open balls in \(Y_ 1\) are arcwise connected. Other sufficient conditions are stated in terms of extendability of continuous functions from zero-subsets of \(X\) into \(Y\) to the whole \(X\).

MSC:

54E52 Baire category, Baire spaces
54C35 Function spaces in general topology
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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