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Article

Adámek, Jiří ; Reiterman, Jan
The category of uniform spaces as a completion of the category of metric spaces. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 33 (1992), issue 4, pp. 689-693
MSC: 18A32, 18A35, 54B30, 54E15, 54E35 | MR 1240190 | Zbl 0804.18001
Keywords:
universal completion; metric space; uniform space
Summary:
A criterion for the existence of an initial completion of a concrete category $\bold K$ universal w.r.t\. finite products and subobjects is presented. For $\bold K=$ metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
References:
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[AHS] Adámek J., Herrlich H., Strecker G.E.: Least and largest initial completion. Comment. Math. Univ. Carolinae 20 (1979), 43-75. MR 0526147
[C] Čech E.: Topological Spaces. Academia Prague, 1966. MR 0211373
[E] Ehersmann A.E.: Partial completions of concrete functors. Cahiers Topo. Géom. Diff. 22 (1981), 315-328. MR 0649079
[H] Herrlich H.: Initial completions. Math. Z. 150 (1976), 101-110. MR 0437614 | Zbl 0319.18001
[PRRS] Pelant J., Reiterman J., Rödl V., Simon P.: Ultrafilters on $ømega $ and atoms in the lattice of uniformities I. Topology and Appl. 30 (1988), 1-17. MR 0964058
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