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

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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. 
@article{SM_2000_191_11_a3,
     author = {Yu. V. Sadovnichii},
     title = {Lifting the functors $U_\tau$ and $U_R$ to the~categories of bounded metric spaces and uniform spaces},
     journal = {Sbornik. Mathematics},
     pages = {1667--1691},
     publisher = {mathdoc},
     volume = {191},
     number = {11},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_11_a3/}
}
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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/