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.

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关于 Pestryakov 定理的推广

1987年，AV Pestryakov证明了Baire类$\alpha$$(\alpha>0)$的所有实值函数空间$B_{\alpha}(X)$的基函数的一系列定理，他推测这些定理中的大多数对于包含 $X$ 中零集特征函数的所有有限线性组合的空间是正确的。在本文中，我们调查 Pestriakov 泛化的哪些定理是有效的。我们还应用选择原理理论证明了函数空间的一些附加命题。