On Orderability of Topological Groups

Abstract

A necessary and sufficient condition for a topological group whose topology can be induced by a total order compatible with the group structure is given and such groups are called ordered or orderable topological groups. A separable totallydisconnected ordered topological group is proved to be non-archimedean metrizable while the converse is shown to be false by means of an example. A necessary and sufficient condition for a no-totally disconnected locally compact abelian group to be orderable

Cite this paper

@inproceedings{Rangan2004OnOO, title={On Orderability of Topological Groups}, author={Geeta Rangan}, year={2004} }