Geodesic
Dense Orderings in the Space of Left-orderings of a Group
Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 393-404

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DOI

Every left-invariant ordering of a group is either discrete, meaning there is a least element greater than the identity, or dense. Corresponding to this dichotomy, the spaces of left, Conradian, and bi-orderings of a group are naturally partitioned into two subsets. This note investigates the structure of this partition, specifically the set of dense orderings of a group and its closure within the space of orderings. We show that for bi-orderable groups, this closure will always contain the space of Conradian orderings—and often much more. In particular, the closure of the set of dense orderings of the free group is the entire space of left-orderings.
DOI : 10.4153/S0008439519000493
Mots-clés : ordered group, space of left-orderings, bi-orderable group 
Clay, Adam; Reimer, Tessa. Dense Orderings in the Space of Left-orderings of a Group. Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 393-404. doi: 10.4153/S0008439519000493
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     year = {2020},
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