# On the Jayne-Rogers theorem

## TL;DR

This paper extends the Jayne-Rogers theorem to a broader class of spaces, showing that $ ext{Δ}^0_2$-measurability coincides with piecewise continuity for mappings from perfectly paracompact, first-countable spaces to regular spaces.

## Contribution

It generalizes the classical Jayne-Rogers theorem to include perfectly paracompact, first-countable spaces, broadening its applicability.

## Key findings

- $ ext{Δ}^0_2$-measurability is equivalent to piecewise continuity in the new setting.
- The result applies to mappings from perfectly paracompact, first-countable spaces.
- Provides a unified framework extending the classical theorem.

## Abstract

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.