Classification of selectors for sequences of dense sets of Baire functions

TL;DR

This paper investigates the existence and properties of selectors for sequences of dense and sequentially dense sets within the space of Baire functions on a Tychonoff space, focusing on topological and functional analysis aspects.

Contribution

It introduces new results on selectors for sequences of dense sets in B(X), advancing understanding of their structure and selection principles in function spaces.

Findings

Established conditions for the existence of selectors in B(X)

Analyzed properties of dense and sequentially dense sets in Baire function spaces

Provided new criteria for selection in topological function spaces

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).