Symmetry conditions on the coincidence of some notions of quasi-uniform completeness (Q925440)

This paper introduces the properties of weakly quiet spaces and *- weakly pair Cauchy bounded spaces, which generalize the notions of quiet spaces and of semisymmetric spaces. The two properties introduced are dovetailed by the results that every weakly quiet space is uniformly weakly regular, and that every uniformly weakly regular *-weakly pair Cauchy bounded half-complete space is weakly quiet. The author shows that the bicompletion of a \(T_0\)-weakly quiet space is its \(T_1\)-half completion and that the bicompletion of a quiet *-weakly pair Cauchy bounded space is its \(D\)-completion.