Can a Borel group be generated by a Hurewicz subspace?

TL;DR

This paper explores the topological properties of sets that generate Borel non-sigma-compact groups, linking these properties to the Scheepers diagram problem within the context of the Cantor group.

Contribution

It formulates three new problems related to the topological characteristics of generating sets for Borel groups, connecting to existing open problems.

Findings

Reformulation of the Scheepers diagram problem for specific subgroups

Identification of topological properties influencing group generation

Introduction of three open problems in the area

Abstract

In this paper we formulate three problems concerning topological properties of sets generating Borel non-sigma-compact groups. In case of the concrete F_\sigma\delta-subgroup of the Cantor group this gives an equivalent reformulation of the Scheepers diagram problem.