International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2007 / Article

Research Article | Open Access

Volume 2007 |Article ID 087592 | https://doi.org/10.1155/2007/87592

Athanasios Andrikopoulos, "Symmetry Conditions on the Coincidence of Some Notions of Quasi-Uniform Completeness", International Journal of Mathematics and Mathematical Sciences, vol. 2007, Article ID 087592, 12 pages, 2007. https://doi.org/10.1155/2007/87592

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

Academic Editor: Etienne E. Kerre
Received06 Feb 2007
Accepted26 Jun 2007
Published19 Aug 2007

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.

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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.


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