Geodesic
A Construction of the Pair Completion of a Quasi-Uniform Space
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 53-59

Voir la notice de l'article provenant de la source Cambridge University Press

Although L. Nachbin introduced the concept of a quasiuniform space in connection with the study of uniform ordered spaces [7], it was A. Császár who first developed a theory of completion for these spaces. In the review of Császár′s work [3], J. Isbell wrote: “A topogenic space is already complete according to the present definition; an unfortunate side effect is that not every convergent filter is Cauchy.” This aspect of Császár′s theory of completeness seems to have stalled the investigation of its applications, so that even in the study of uniform ordered spaces Császár′s important work has often been overlooked. While it may have seemed that Isbell had pointed out the Achilles′ heel of Császár′s theory, in this paper we outline a construction of Császár′s completion for quasi-uniform spaces, which differs from Császár′s original construction and the construction given by S. Salbany [8], in which Isbell′s objection does not obtain. 
Lindgren, William F.; Fletcher, Peter. A Construction of the Pair Completion of a Quasi-Uniform Space. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 53-59. doi: 10.4153/CMB-1978-009-2
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