International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 87592, 12 pages
Symmetry Conditions on the Coincidence of Some Notions of Quasi-Uniform Completeness
Department of Economics, University of Ioannina, Ioannina 45110, Greece
Received 6 February 2007; Accepted 26 June 2007
Academic Editor: Etienne E. Kerre
Copyright © 2007 Athanasios Andrikopoulos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We generalize the notions of quietness and semisymmetry defined by
Doitchinov (1991) and Deák (1991) and
we study the role of these extended notions on the coincidence of some well-known
quasi-uniform completeness. In particular, it is shown that the bicompletion
coincides (up to quasi-uniformism) with the standard -completion in quiet -weakly pair Cauchy bounded quasi-uniform spaces and it coincides with -half-com- pletion defined by Romaguera and Sánchez-Granero
in -weakly quiet quasi-uniform spaces.