Geodesic
Spaces with a Unique Uniformity
Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 1001-1009

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

The major results in this paper are nine characterizations of completely regular spaces with a unique compatible uniformity. All prior results of this type assumed that the space is Tychonoff (i.e., completely regular and Hausdorff) until the appearance of a companion paper [9] which began this study. The more important characterizations use quasi-uniqueness of R 1-compactifications which relate to uniqueness of T 2-comPactifications. The features of the other characterizations are: (i) compact subsets linked to Cauchy filters, (ii) C- and C*-embeddings, and (iii) lifting continuous maps to uniformly continuous maps.Section 2 contains information on T 0-identification spaces which we will use later in the paper. In Section 3 several properties of uniform identification spaces are developed so that they can be used later. The nine characterizations are established in Section 4. Also it is shown that a space with a unique compatible uniformity is normal if and only if each of its closed subspaces has a unique compatible uniformity. 
Warren, Richard H. Spaces with a Unique Uniformity. Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 1001-1009. doi: 10.4153/CJM-1983-055-9
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