Skip to main content
Log in

Strong collective normality and countable compactness in free topological groups

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. H. J. Cohen, “Sur une problème de M. Dieudonné,” C. R. Acad. Sci.,234, 290–292 (1952).

    Google Scholar 

  2. H. L. Shapico and F. A. Smith, “Paracompactness in uniform spaces,” Topol. Proc.,3, 179–197 (1978).

    Google Scholar 

  3. M. I. Graev, “Free topological groups,” Izv. Akad. Nauk SSSR, Ser. Mat.,12, 270–324 (1948).

    Google Scholar 

  4. I. Glicksberg, “Stone-Čech compactifications of products,” Trans. Am. Math. Soc.,90, 369–382 (1959).

    Google Scholar 

  5. N. Noble, “Products with closed projections,” Trans. Am. Math. Soc.,140, 381–391 (1969).

    Google Scholar 

  6. H. Tamano, “On paracompactness,” Pac. J. Math.,10, 1043–1047 (1960).

    Google Scholar 

  7. R. Engelking, General Topology, PWN, Warsaw (1977).

    Google Scholar 

  8. V. G. Pestov, “Some properties of free topological groups,” Vestn. Mosk. Univ., Mat. Mekh., No. 1, 35–37 (1982).

    Google Scholar 

  9. M. G. Tkachenko, “The Suslin property in free topological groups over bicompacts,” Mat. Zametki,34, No. 4, 601–607 (1983).

    Google Scholar 

  10. E. V. Shchepin, “Real functions and canonical sets in Tikhonov products and topological groups,” Usp. Mat. Nauk,31, No. 6, 17–27 (1976).

    Google Scholar 

  11. A. V. Arkhangel'skii, “Relations between invariant topological groups and their subspaces,” Usp. Mat. Nauk,35, No. 3, 3–22 (1980).

    Google Scholar 

  12. N. V. Velichko, “A remark on plumed spaces,” Czechoslovak. Math. J.,25, No. 1, 8–19 (1975).

    Google Scholar 

  13. V. K. Bel'nov, “The dimension of free topological groups,” Thesis of the IVth Tiraspol'skii Symposium on General Topology and Its Applications, 1979, Shtiintsa, pp. 14–15 (1979).

  14. P. S. Aleksandrov and B. A. Pasynkov, Introduction to the Theory of Dimension [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  15. M. G. Tkachenko, “Zero-dimensional topological groups,” Proceedings of the Leningrad International Topological Conference, Nauka, Leningrad (1983), pp. 113–118.

    Google Scholar 

  16. A. V. Arkhangel'skii, “Supplement” to General Topology by J. Kelley [Russian translation], 2nd ed., Nauka, Moscow (1981), pp. 356–409.

    Google Scholar 

  17. J. Mack, S. A. Morris, and E. T. Ordman, “Free topological groups and the projective dimension of a locally compact Abelian group,” Proc. Am. Math. Soc.,40, 303–308 (1973).

    Google Scholar 

  18. V. G. Pestov, “The construction and inclusions of topological groups,” Deposition in VINITI 3.04.81, No. 1495-81, Moscow (1981).

  19. T. Fay, E. Ordman, and B. V. S. Thomas, “The free topological group over the rationals,” Gen. Topol. Appl.,10, No. 1, 33–47 (1979).

    Google Scholar 

  20. S. P. Franklin, “Spaces in which sequences suffice. II,” Fundam. Math.,57, No. 1, 51–56 (1967).

    Google Scholar 

  21. S. S. Dumitrashku, “Universal topological algebras with continuous signature,” Candidate's Dissertation, Physical-Mathematical Sciences, Kishinev (1983).

Download references

Authors

Additional information

Balakovo, Saratovskii Region. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 5, pp. 167–177, September–October, 1987.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tkachenko, M.G. Strong collective normality and countable compactness in free topological groups. Sib Math J 28, 824–832 (1987). https://doi.org/10.1007/BF00969330

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00969330

Keywords

Navigation