The category of uniform spaces as a completion of the category of metric spaces
نویسندگان
چکیده
A criterion for the existence of an initial completion of a concrete category K universal w.r.t. finite products and subobjects is presented. For K = metric spaces and uniformly continuous maps this completion is the category of uniform spaces.
منابع مشابه
Uniformities in fuzzy metric spaces
The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...
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