On the product of two \(b_ f\)-spaces (Q1310436)

If \(b\) is a system of sets in a completely regular Hausdorff space \(X\), then \(X\) is called a \(b_ f\)-space if a real-valued function on \(X\) is continuous provided its restrictions to each member of \(b\) can be continuously extended to \(X\). For the case \(b\) consists of relatively pseudocompact subsets, the main results describe when a product of two spaces is a \(b_ f\)-space, and characterize those spaces \(X\) such that \(X \times Y\) is a \(b_ f\)-space whenever \(Y\) is.