Geodesic
Some Results on Quasi-Uniform Spaces
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 39-51

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

Constructions are made of a T 1 space which does not have a T 1 completion and of a quasi-uniform space which is complete, but not strongly complete. An example relating to a completion due to Popa is given. An alternate definition for Cauchy filter, called C-filter, is examined and a construction of a C-completion is given. We discuss quasi-pseudometrics over a Tikhonov semifield R Δ. Every topological space is quasi-pseudometrizable over a suitable R Δ. It is shown that if a quasi-pseudometric space over R Δ is complete, the corresponding quasi-uniform structure is C-complete. A general method for constructing compatible quasiuniform structures is given. 
Carter, Karen S.; Hicks, T. L. Some Results on Quasi-Uniform Spaces. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 39-51. doi: 10.4153/CMB-1976-005-6
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