On orderability of topological groups

G. Rangan

International Journal of Mathematics and Mathematical Sciences, 1985, vol. 8, 1-8

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.

Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:323070

DOI: 10.1155/S0161171285000837

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