On the Jayne-Rogers theorem

Abstract

In 1982, J.E. Jayne and C.A. Rogers proved that a mapping $f:X\to Y$ of an absolute Souslin-F set X to a metric space Y is ${\Delta }_2^0$-measurable if and only if it is piecewise continuous. We now give a similar result for a perfectly paracompact first-countable space X and a regular space Y.

6 pages. arXiv admin note: text overlap with arXiv:1112.0350 by other authors