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
@article{SMJ2_1998_24_1_a7,
author = {K\"unzi, Hans-Peter and Romaguera, Salvador and Sipacheva, Ol{\textquoteright}ga},
title = {The {Doitchinov} {Completion} of a {Regular} {Paratopological} {Group}},
journal = {Serdica Mathematical Journal},
pages = {73--88},
publisher = {mathdoc},
volume = {24},
number = {1},
year = {1998},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SMJ2_1998_24_1_a7/}
}
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 SP - 73 EP - 88 VL - 24 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SMJ2_1998_24_1_a7/ LA - en ID - SMJ2_1998_24_1_a7 ER -
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/