Infinite products of quasi-continuous functions
Recall that a function \(f:X\to Y\) between topological spaces is \textit{quasi-continuous} provided \(f^{-1}(V)\subset\overline{\text{Int}(f^{-1}(V))}\) for each open \(V\subset Y\). It is shown that a function \(f:X\to\mathbb R\), where \(X\) is metric, is an infinite product of a sequence of quasi-continuous functions if and only if \(f\) is a Baire function and \(\overline{f^{-1}(0,\infty)}\cap\overline{f^{-1}(-\infty,0)}\setminus f^{-1}(0)\) is meagre. Consequently a cliquish function \(X\to\mathbb R\), \(X\) metric, is such a product.
scientific article; zbMATH DE number 5625510