International Journal of Mathematics and Mathematical Sciences 
Volume 2007 (2007), Article ID 87592, 12 pages
doi:10.1155/2007/87592
Research Article

Symmetry Conditions on the Coincidence of Some Notions of Quasi-Uniform Completeness

Athanasios Andrikopoulos

 Department of Economics, University of Ioannina, Ioannina 45110, Greece
Received 6 February 2007; Accepted 26 June 2007

Recommended by Etienne E. Kerre

Abstract

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 D-completion in quiet ⋆-weakly pair Cauchy bounded quasi-uniform spaces and it coincides with ⋆-half-com- pletion defined by Romaguera and Sánchez-Granero (2002), in T0-weakly quiet quasi-uniform spaces.