Maximal additive and maximal multiplicative family for the class of simply continuous functions (Q1890617)

Let \(X\) be a topological space. A function \(f\) from \(X\) to \(\mathbb{R}\) is simply continuous if for each open set \(V\) \(f^{-1}(V)\) is the union of an open and of a nowhere dense set. In this paper the maximal (additive and multiplicative) families are examined.