On generalization of theorems of Pestryakov

In 1987, A.V. Pestryakov proved a series of theorems for cardinal functions of the space $B_α(X)$ 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 Pestriakov generalizations are valid. Also we prove some additional propositions for function spaces applying the theory of selection principles.

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