On generalization of theorems of Pestryakov

Abstract

In 1987 A.V. Pestryakov proved a series of theorems for cardinal functions of the space Bα(X) of all real-valued functions of Baire class α (α>0), and he conjectured that most of these theorems are true for spaces containing all finite linear combinations of characteristic functions of zero-sets in X. In this paper we investigate for which theorems of Pestryakov generalizations are valid. Also we prove some additional propositions for function spaces applying the theory of selection principles. © 2020