Geodesic
Lifting the functors $U_\tau$ and $U_R$ to the categories of bounded metric spaces and uniform spaces
Sbornik. Mathematics, Tome 191 (2000) no. 11, pp. 1667-1691 Cet article a éte moissonné depuis la source Math-Net.Ru

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Metric and uniform properties of the unit ball functors $U_\beta$, $U_R$, $U_\tau$ of measures with compact support, Radon measures, and $\tau$-additive measures, respectively, are studied. It is proved that these functors can be lifted to the category $\mathbf{BMetr}$ of bounded metric spaces, $\mathbf{BMetr}_u$ of bounded metric spaces and uniformly continuous maps, and $\mathbf{Unif}$ of uniform spaces. Additionally, it is shown that the functor $U_\tau$ preserves the completeness property of metric spaces. 
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Yu. V. Sadovnichii. Lifting the functors $U_\tau$ and $U_R$ to the categories of bounded metric spaces and uniform spaces. Sbornik. Mathematics, Tome 191 (2000) no. 11, pp. 1667-1691. http://geodesic.mathdoc.fr/item/SM_2000_191_11_a3/

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