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of their metric balls, and because of this alternative definition
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of its points, and assigns to each metric map the underlying set-theoretic function. This functor is
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is a monomorphism and an epimorphism, but it is clearly not an isomorphism; this example shows that
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is not the only category whose objects are metric spaces; others include the category of
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of the spaces as its points; the distance in the product space is given by the
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between metric spaces that do not increase any pairwise distance) as its
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of two metric maps is again a metric map. It was first considered by
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as a category; they may also be defined intrinsically in terms of a
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of the distances in the base spaces. That is, it is the
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272:assigns to each metric space the underlying
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404:(2009), "Category of metric spaces",
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323: – category in mathematics
224:is a metric space that has the
376:Pacific Journal of Mathematics
336:Category of topological spaces
301:uniformly continuous functions
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471:Categories in category theory
356: – Topological category
370:; Panitchpakdi, P. (1956),
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407:Encyclopedia of Distances
309:quasi-Lipschitz mappings
184:, prior to the study of
178:injective metric spaces
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208:Products and functors
434:Comment. Math. Helv.
307:and the category of
220:of metric spaces in
141:metric space is the
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398:Deza, Michel Marie
321:Category of groups
303:, the category of
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194:hyperconvex spaces
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286:concrete category
261:forgetful functor
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226:cartesian product
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