  In 1982, J.E. Jayne and C.A. Rogers proved that a mapping $f \colon X
\rightarrow Y$ of an absolute Souslin-F set X to a metric space Y is
$\Delta^0_2$-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.
