∗-half completeness in quasi-uniform spaces

Abstract

Abstract.Romaguera and have introduced the notion of T1 * -half completion and used it to see when a quasi-uniform space has a * -compactification. In this paper, for any quasi-uniform space, we construct a * -half completion, called standard * -half completion. The constructed * -half completion coincides with the usual uniform completion in the uniform spaces and is the unique (up to quasi-isomorphism) T1* -half completion of a symmetrizable quasi-uniform space. Moreover, it constitutes a * -compactification for * -Cauchy bounded quasi-uniform spaces. Finally, we give an example which shows that the standard * -half completion differs from the bicompletion construction.2000 AMS Classification: 54E15, 54D35.