Note on limits of simply continuous and cliquish functions

Abstract

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 {fn:n≥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)→Y is cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.