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Cartesian closed hull for metric spaces. (English) Zbl 0702.18002
Let Dist be the category whose objects are pairs (X,d) where X is a set, $$d: X\times X\to [0,+\infty]$$ is a mapping such that $$d(x,x)=0$$ for every $$x\in X$$, $$d(x,y)=d(y,x)$$ for every pair x,y$$\in X$$; morphisms from (X,d) to (Y,e) are all mappings $$f:X\to Y$$ such that e(f(x),f(y))$$\leq d(x,y)$$ for every pair x,y$$\in X$$. The category Dist is cartesian closed topological. Let $$Metr_ n$$ be the full subcategory of Dist whose objects form all metric spaces. The aim of the paper is a description of the cartesian closed topological hull of $$Metr_ n$$ in Dist.
Reviewer: V.Koubek

##### MSC:
 18B30 Categories of topological spaces and continuous mappings (MSC2010) 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.) 54E40 Special maps on metric spaces
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