Yu. V. Sadovnichii, “Lifting the functors $U_\tau$ and $U_R$ to the categories of bounded metric spaces and uniform spaces”, Mat. Sb., 2000, Volume 191, Number 11,Pages 79

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

Yu. V. Sadovnichii

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.

UDC: 515.12

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

Received: 17.12.1999

DOI: 10.4213/sm522