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On orderability of topological groups

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  • G. Rangan

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.

Suggested Citation

  • G. Rangan, 1985. "On orderability of topological groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:323070
    DOI: 10.1155/S0161171285000837
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