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

DOI: 10.1155/2007/87592

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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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