Generating countable groups by discrete subsets

TL;DR

This paper proves that every countable topological group can be generated by a closed discrete subset such that the group equals the product of this subset with its inverse.

Contribution

It establishes a universal property for countable topological groups regarding generation by closed discrete subsets.

Findings

Existence of such subsets in all countable topological groups

The subset can be chosen to be closed and discrete

Group equals the product of the subset and its inverse

Abstract

Every countable topological group $G$ has a closed discrete subset $A$ such that $G=AA^{-1}.$