International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 747-754
doi:10.1155/S0161171285000837

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 totally disconnected 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 is also given.