International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 747-754
On orderability of topological groups
The Ramanujan Institute, University of Madras, Madras 5, India
Received 15 October 1984
Copyright © 1985 G. Rangan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.