Locally Compact Topological Groups and Cofinal Completeness

It is proved that a Tychonoff topological group is locally compactif and only if it is of pointwise countable type and its leftuniformity is cofinally complete. From this result a characterizationis derived of those T₀ paratopological groups (X, ) of pointwisecountable type for which (X, ^–1) is locally compactand also a characterization is deduced of locally pseudocompacttopological groups in terms of cofinal completeness. Also characterizedare the Tychonoff topological groups of pointwise countabletype for which their left uniformity has property U. Finally,cofinal completeness of the Hausdorff–Bourbaki uniformityof a topological group is studied.