Note on limits of simply continuous and cliquish functions
Summary: The main result of this paper is that any function \(f\) defined on a perfect Baire space \((X,T)\) with values in a separable metric space \(Y\) is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence \(\{f_ n : n \geq 1\}\) of simply continuous functions. This result is obtained by a change of a topology on \(X\) and showing that a function \(f:(X,T) \to Y\) is cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.
scientific article; zbMATH DE number 650812