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

Kyrylo Muliarchyk; Serhii Dovhyi

paper

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

arXiv:1812.06058

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 $L O (F_{2})$ has no isolated points, where $F_{2}$ is a free group on two generators. In this paper we show that $O (F_{2})$ has no isolated points as well.