Atlas home || Conferences | Abstracts | about Atlas

II Congreso Iberoamericano de Topología y sus Aplicaciones
March 20-22, 1997

Morelía, Mexico

Organizers
Salvador García-Ferreira, Daniel Juan Pineda, Sergio Macías Alvarez, Max Neumann Coto, María L. Pérez Seguí, Salvador Romaguera Bonilla, Manuel Sanchis López, Angel Tamariz Mascarúa, M. G. Tkachenko, Javier F. Trigos Arrieta

View Abstracts
Conference Homepage

The Doitchinov completion of a regular paratopological group
by
Hans-Peter A. Künzi
University of Berne
Coauthors: Salvador Romaguera, Ol'ga V. Sipacheva

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 an Abelian group. Furthermore [^(UB)] is the two-sided quasi-uniformity of ([^G], ·).

These results generalize in an appropriate way important results about topological groups to Abelian 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.

Date received: February 9, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caak-19.