Research Article | Open Access
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
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 (2002), in -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.