# A game characterizing Baire class 1 functions

## TL;DR

This paper generalizes a game-theoretic characterization of Baire class 1 functions from zero-dimensional Polish spaces to arbitrary Polish spaces, providing a new tool for analyzing these functions.

## Contribution

It introduces a new game for arbitrary Polish spaces that characterizes Baire class 1 functions, extending previous zero-dimensional results.

## Key findings

- Player II has a winning strategy iff the function is Baire class 1
- Reproves a result on first return recoverable functions using the game strategy
- Provides a new characterization of Baire class 1 functions in general Polish spaces

## Abstract

Duparc introduced a two-player game for a function $f$ between zero-dimensional Polish spaces in which Player II has a winning strategy iff $f$ is of Baire class 1. We generalize this result by defining a game for an arbitrary function $f : X \to Y$ between arbitrary Polish spaces such that Player II has a winning strategy in this game iff $f$ is of Baire class 1. Using the strategy of Player II, we reprove a result concerning first return recoverable functions.