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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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