Classification of selectors for sequences of dense sets of Baire functions

Abstract

For a Tychonoff space X, we denote by B(X) the space of all Baire functions on X with the topology of pointwise convergence. In this paper we investigate selectors for sequences of countable dense and countable sequentially dense sets of the space B(X). We give the characteristics of the selection principles S 1 (P,Q) and S fin (P,Q) for P,Q∈{D, S, A}, where • D — the family of all countable dense subsets of B(X); • S — the family of all countable sequentially dense subsets of B(X); • A — the family of all countable 1-dense subsets of B(X), through the selection principles of X. © 2019