Geodesic
A Note on Totally Bounded Quasi-Uniformities
Serdica Mathematical Journal, Tome 24 (1998) no. 1, pp. 95-98

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We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity. The proof was obtained about ten years ago, but never published. In the mean-time several stronger results have been obtained by more direct arguments [8, 9, 10]. In particular it follows from Künzi’s [8] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Déak [10] observed that even each totally bounded Cauchy quasi-uniformity is a uniformity.
Keywords: D-Complete, Quite 
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Fletcher, P.; Hunsaker, W. A Note on Totally Bounded Quasi-Uniformities. Serdica Mathematical Journal, Tome 24 (1998) no. 1, pp. 95-98. http://geodesic.mathdoc.fr/item/SMJ2_1998_24_1_a9/