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

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.