Geodesic
The Doitchinov Completion of a Regular Paratopological Group
Serdica Mathematical Journal, Tome 24 (1998) no. 1, pp. 73-88.

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We show that the two-sided quasi-uniformity UB of a regular paratopological group (G, ·) is quiet. The Doitchinov completion (G, UB ) of (G, UB ) can be considered a paratopological group containing G as a doubly dense subgroup whenever G is Abelian. Furthermore UB is the two-sided quasi-uniformity of (G, ·). These results generalize in an appropriate way important results about topological groups to regular paratopological groups. A counterexample dealing with the non-Abelian case is presented. Furthermore we give conditions, depending on quasi-uniform completeness properties, under which a paratopological group is a topological group.
Keywords: Quasi-Uniformity, Quiet, Doitchinov Complete, Balanced, Left K-Complete, Paratopological Group 
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Künzi, Hans-Peter; Romaguera, Salvador; Sipacheva, Ol’ga. The Doitchinov Completion of a Regular Paratopological Group. Serdica Mathematical Journal, Tome 24 (1998) no. 1, pp. 73-88. http://geodesic.mathdoc.fr/item/SMJ2_1998_24_1_a7/