Ji\v r\'\i {} Ad\'amek, Jan Reiterman
The category of uniform spaces as a completion of the category of metric spaces

Abstract: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.

Keywords: universal completion, metric space, uniform space
AMS Subject Classification: 18A35, 54B30, 54E15

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