Abstract
A topological space \(X\) has the Baire property if any countable intersection of open dense subsets of \(X\) is dense in \(X\) . An interesting problem in the theory of function spaces is that of characterizing the Baire property of a function space in terms of a topological property of the supports of functions.
A solution of this problem for the space \(B_{\alpha}(X,\{0,1\})\) of Baire class \(\alpha\) indicator functions, where \(1\leq \alpha\leq \omega_1\) , is presented. Namely, given a Tychonoff space \(X\) , a criterion for the space \(B_{\alpha}(X,\{0,1\})\) to have the Baire property in terms of a topological property of \(X\) is obtained. This result answers a question of T. Banakh and S. Gabriyelyan in the class of spaces of Baire indicator functions.
