∗-half completeness in quasi-uniform spaces


  • Athanasios Andrikopoulos University of Ioannina




Quasi-uniform, ∗-half completion, ∗-compactification


Romaguera and Sánchez-Granero (2003) 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.


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Author Biography

Athanasios Andrikopoulos, University of Ioannina

Department of Economics


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How to Cite

A. Andrikopoulos, “∗-half completeness in quasi-uniform spaces”, Appl. Gen. Topol., vol. 10, no. 1, pp. 29–37, Apr. 2009.



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