On the topology of the space of bi-orderings of a free group on two generators

Serhii Dovhyi; Kyrylo Muliarchyk

paper

On the topology of the space of bi-orderings of a free group on two generators

arXiv:2101.04637

Abstract

Let $G$ be a group. We can topologize the spaces of left-orderings $L O (G)$ and bi-orderings $O (G)$ of $G$ with the product topology. These spaces may or may not have isolated points. It is known that $L O (F_{n})$ has no isolated points, where $F_{n}$ is a free group on $n \geq 2$ generators. In this paper, we show that $O (F_{n})$ has no isolated points as well.

arXiv commentduplicate of arXiv:1812.06058