# On generalization of theorems of Pestryakov

## TL;DR

This paper examines the extent to which Pestryakov's theorems on cardinal functions of Baire class function spaces can be generalized to larger spaces, using selection principles to establish new results.

## Contribution

It identifies which of Pestryakov's theorems extend to spaces containing finite linear combinations of characteristic functions of zero-sets, and introduces new propositions via selection principles.

## Key findings

- Certain Pestryakov theorems are valid for broader function spaces.
- New propositions for function spaces are established using selection principles.
- The paper clarifies the scope of generalizations of Pestryakov's results.

## Abstract

In 1987, A.V. Pestryakov proved a series of theorems for cardinal functions of the space $B_{\alpha}(X)$ of all real-valued functions of Baire class $\alpha$ $(\alpha> 0)$, 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.