The space of left orders of a group is either finite or uncountable

Abstract

Let G be a group and let O_G denote the set of left orderings on G. Then O_G can be topologized in a natural way, and we shall study this topology to show that O_G can never be countably infinite. This paper retrieves correct parts of the withdrawn paper arXiv:math/0607470.

4 pages

Cited by in corpus (7)

• About left orders in Garside groups
• Dehornoy-like left orderings and isolated left orderings
• Borel structures on the space of left-orderings
• Orderings and flexibility of some subgroups of $Home{o}_{+}(\mathbb{R})$
• Dense orderings in the space of left-orderings of a group
• Spaces of orders of some one-relator groups
• Space of orders with finite Cantor-Bendixson rank