Abstract
In this paper, we study the questions of uniform and topological completeness of functors of the unit ball U τ and U R of τ-additive measures and Radon measures respectively.
Similar content being viewed by others
REFERENCES
P. S. Alexandrov and B. A. Pasynkov, An Introduction to Dimension Theory [in Russian], Nauka, Moscow (1973).
A. V. Arkhangelskii, “On a class of spaces containing all metric and all locally bicompact spaces,” Mat. Sb., 67,No. 1, 55–85 (1965).
T. O. Banach, “Topology of spaces of probability measures. II: Barycenters of probability Radon measures and metrization of the functors P τ and \(\hat P\),” Matem. Stud. Pratsi. Lvivsk. Matem. T-va, No. 5, 88–106 (1995).
V. S. Varadarayn, “Measures on topological spaces,” Mat. Sb., 55,No. 1, 35–100 (1961).
Yu. V. Sadovnichy, “On some categorical properties of the functor U τ,” Vestnik Mosk. Univ., Ser. I, Mat., Mekh., No. 3, 38–42 (1999).
Yu. V. Sadovnichy, “Lifting of the functors U τ and U R to the category of bounded uniform spaces,” Mat. Sb., 191,No. 11, 79–104 (2000).
V. V. Fedorchuk, “Topological completeness of spaces of measures,” Izv. Ros. Akad. Nauk, Ser. Mat., 63,No. 4, 207–223 (1999).
V. V. Fedorchuk and V. V. Filippov, General Topology. Basic Structures, Izd. Mosk. Univ., Moscow (1988).
J. Dieudonné, “Sur les espaces uniformes complets,” Ann. Sci. École Norm. Sup., 56, 277–291 (1939).
R. Engelking, General Topology, Berlin (1989).
V. V. Fedorchuk, “On a preservation of completeness of uniform spaces by the functor P τ,” Topol. Appl., 91, 25–45 (1999).
R. G. Gardner and W. F. Pfeffer, “Borel measures,” in: Handbook of Set-Theoretic Topology, Elsevier Science Publishers B. V. (1984), pp. 961–1043.
E. Hewitt, “Rings of real-valued continuous functions. I,” Trans. Amer. Math. Soc., 64, 45–99 (1948).
J. Nagata, “On topological completeness,” J. Math. Soc. Japan, 2, 44–47 (1950).
Yu. V. Sadovnichy, “On some categorical properties of the functor U R,” Topol. Appl., 107, 131–145 (2000).
T. Shirota, “A class of topological spaces,” Osaka J. Math., 4, 23–40 (1952).
R. Solovay and S. Tannenbaum, “Iterated Cohen extensions and Suslin's problem,” Ann. Math., 94, 201–245 (1971).
Rights and permissions
About this article
Cite this article
Sadovnichy, Y.V. On Completeness Properties of Functors of the Unit Ball of Borel Measures. Journal of Mathematical Sciences 120, 1442–1452 (2004). https://doi.org/10.1023/B:JOTH.0000016060.81936.48
Issue Date:
DOI: https://doi.org/10.1023/B:JOTH.0000016060.81936.48