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 Mat. Sb., 2000, Volume 191, Number 11, Pages 79–104 (Mi msb522)

Lifting the functors $U_\tau$ and $U_R$ to the categories of bounded metric spaces and uniform spaces

M. V. Lomonosov Moscow State University

Abstract: 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.

DOI: https://doi.org/10.4213/sm522

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English version:
Sbornik: Mathematics, 2000, 191:11, 1667–1691

Bibliographic databases:

UDC: 515.12
MSC: Primary 28A33, 54E35, 54E15; Secondary 18Bxx

Citation: Yu. V. Sadovnichii, “Lifting the functors $U_\tau$ and $U_R$ to the categories of bounded metric spaces and uniform spaces”, Mat. Sb., 191:11 (2000), 79–104; Sb. Math., 191:11 (2000), 1667–1691

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb522
• https://doi.org/10.4213/sm522
• http://mi.mathnet.ru/eng/msb/v191/i11/p79

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Yu. V. Sadovnichii, “On soft mappings of the unit ball of Borel measures”, J. Math. Sci., 136:5 (2006), 4156–4165
2. Sadovnichii, YV, “On topological and categorical properties of the functors M-tau and M-R”, Doklady Mathematics, 75:3 (2007), 349
3. Djabbarov G., “Metrization of the space of weakly additive positively-homogeneous functionals”, Topology Appl., 221 (2017), 133–143
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