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On Completeness Properties of Functors of the Unit Ball of Borel Measures

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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.

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REFERENCES

  1. P. S. Alexandrov and B. A. Pasynkov, An Introduction to Dimension Theory [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  2. A. V. Arkhangelskii, “On a class of spaces containing all metric and all locally bicompact spaces,” Mat. Sb., 67,No. 1, 55–85 (1965).

    Google Scholar 

  3. 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).

    Google Scholar 

  4. V. S. Varadarayn, “Measures on topological spaces,” Mat. Sb., 55,No. 1, 35–100 (1961).

    Google Scholar 

  5. Yu. V. Sadovnichy, “On some categorical properties of the functor U τ,” Vestnik Mosk. Univ., Ser. I, Mat., Mekh., No. 3, 38–42 (1999).

    Google Scholar 

  6. 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).

    Google Scholar 

  7. V. V. Fedorchuk, “Topological completeness of spaces of measures,” Izv. Ros. Akad. Nauk, Ser. Mat., 63,No. 4, 207–223 (1999).

    Google Scholar 

  8. V. V. Fedorchuk and V. V. Filippov, General Topology. Basic Structures, Izd. Mosk. Univ., Moscow (1988).

    Google Scholar 

  9. J. Dieudonné, “Sur les espaces uniformes complets,” Ann. Sci. École Norm. Sup., 56, 277–291 (1939).

    Google Scholar 

  10. R. Engelking, General Topology, Berlin (1989).

  11. V. V. Fedorchuk, “On a preservation of completeness of uniform spaces by the functor P τ,” Topol. Appl., 91, 25–45 (1999).

    Google Scholar 

  12. R. G. Gardner and W. F. Pfeffer, “Borel measures,” in: Handbook of Set-Theoretic Topology, Elsevier Science Publishers B. V. (1984), pp. 961–1043.

  13. E. Hewitt, “Rings of real-valued continuous functions. I,” Trans. Amer. Math. Soc., 64, 45–99 (1948).

    Google Scholar 

  14. J. Nagata, “On topological completeness,” J. Math. Soc. Japan, 2, 44–47 (1950).

    Google Scholar 

  15. Yu. V. Sadovnichy, “On some categorical properties of the functor U R,” Topol. Appl., 107, 131–145 (2000).

    Google Scholar 

  16. T. Shirota, “A class of topological spaces,” Osaka J. Math., 4, 23–40 (1952).

    Google Scholar 

  17. R. Solovay and S. Tannenbaum, “Iterated Cohen extensions and Suslin's problem,” Ann. Math., 94, 201–245 (1971).

    Google Scholar 

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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

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  • DOI: https://doi.org/10.1023/B:JOTH.0000016060.81936.48

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