Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/547

 Title: The Doitchinov Completion of a Regular Paratopological Group Authors: Künzi, Hans-PeterRomaguera, SalvadorSipacheva, Ol’ga Keywords: Quasi-UniformityQuietDoitchinov CompleteBalancedLeft K-CompleteParatopological 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. URI: http://hdl.handle.net/10525/547 ISSN: 1310-6600 Appears in Collections: Volume 24 Number 1

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