Quasi-Uniformity Quiet Doitchinov Complete Balanced Left K-Complete Paratopological Group
Issue Date:
1998
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 24, No 1, (1998), 73p-88p
Abstract:
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.
Description:
In memory of Professor D. Doitchinov
∗ This paper was written while the first author was supported by the Swiss National Science
Foundation under grants 21–30585.91 and 2000-041745.94/1 and by the Spanish Ministry of
Education and Sciences under DGES grant SAB94-0120. The second author was supported
under DGES grant PB95-0737. During her stay at the University of Berne the third author
was supported by the first author’s grant 2000-041745.94/1 from the Swiss National Science
Foundation.
