On the Jayne–Rogers theorem

Abstract

J. E. Jayne and C. A. Rogers [3] proved that a mapping $${f \colon {X \rightarrow Y}}$$ of an absolute Souslin- $${\mathcal{F}}$$ set X to a metric space Y is $${\mathbf{\Delta}^0_2}$$ -measurable if and only if it is piecewise continuous. We give a similar result for a perfectly paracompact first-countable space X and a regular space Y.