The Doitchinov Completion of a Regular Paratopological Group

Künzi, Hans-Peter, Romaguera, Salvador, and Sipacheva, Ol’ga. "The Doitchinov Completion of a Regular Paratopological Group." Serdica Mathematical Journal 24.1 (1998): 73-88. <http://eudml.org/doc/11579>.

@article{Ku1998,
abstract = {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.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.},
author = {Künzi, Hans-Peter, Romaguera, Salvador, Sipacheva, Ol’ga},
journal = {Serdica Mathematical Journal},
keywords = {Quasi-Uniformity; Quiet; Doitchinov Complete; Balanced; Left K-Complete; Paratopological Group; quasi-uniformity; quiet; Doitchinov complete; balanced, left -complete},
language = {eng},
number = {1},
pages = {73-88},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {The Doitchinov Completion of a Regular Paratopological Group},
url = {http://eudml.org/doc/11579},
volume = {24},
year = {1998},
}

TY - JOUR
AU - Künzi, Hans-Peter
AU - Romaguera, Salvador
AU - Sipacheva, Ol’ga
TI - The Doitchinov Completion of a Regular Paratopological Group
JO - Serdica Mathematical Journal
PY - 1998
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 24
IS - 1
SP - 73
EP - 88
AB - 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.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.
LA - eng
KW - Quasi-Uniformity; Quiet; Doitchinov Complete; Balanced; Left K-Complete; Paratopological Group; quasi-uniformity; quiet; Doitchinov complete; balanced, left -complete
UR - http://eudml.org/doc/11579
ER -