Literature Cited
H. J. Cohen, “Sur une problème de M. Dieudonné,” C. R. Acad. Sci.,234, 290–292 (1952).
H. L. Shapico and F. A. Smith, “Paracompactness in uniform spaces,” Topol. Proc.,3, 179–197 (1978).
M. I. Graev, “Free topological groups,” Izv. Akad. Nauk SSSR, Ser. Mat.,12, 270–324 (1948).
I. Glicksberg, “Stone-Čech compactifications of products,” Trans. Am. Math. Soc.,90, 369–382 (1959).
N. Noble, “Products with closed projections,” Trans. Am. Math. Soc.,140, 381–391 (1969).
H. Tamano, “On paracompactness,” Pac. J. Math.,10, 1043–1047 (1960).
R. Engelking, General Topology, PWN, Warsaw (1977).
V. G. Pestov, “Some properties of free topological groups,” Vestn. Mosk. Univ., Mat. Mekh., No. 1, 35–37 (1982).
M. G. Tkachenko, “The Suslin property in free topological groups over bicompacts,” Mat. Zametki,34, No. 4, 601–607 (1983).
E. V. Shchepin, “Real functions and canonical sets in Tikhonov products and topological groups,” Usp. Mat. Nauk,31, No. 6, 17–27 (1976).
A. V. Arkhangel'skii, “Relations between invariant topological groups and their subspaces,” Usp. Mat. Nauk,35, No. 3, 3–22 (1980).
N. V. Velichko, “A remark on plumed spaces,” Czechoslovak. Math. J.,25, No. 1, 8–19 (1975).
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).
P. S. Aleksandrov and B. A. Pasynkov, Introduction to the Theory of Dimension [in Russian], Nauka, Moscow (1973).
M. G. Tkachenko, “Zero-dimensional topological groups,” Proceedings of the Leningrad International Topological Conference, Nauka, Leningrad (1983), pp. 113–118.
A. V. Arkhangel'skii, “Supplement” to General Topology by J. Kelley [Russian translation], 2nd ed., Nauka, Moscow (1981), pp. 356–409.
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).
V. G. Pestov, “The construction and inclusions of topological groups,” Deposition in VINITI 3.04.81, No. 1495-81, Moscow (1981).
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).
S. P. Franklin, “Spaces in which sequences suffice. II,” Fundam. Math.,57, No. 1, 51–56 (1967).
S. S. Dumitrashku, “Universal topological algebras with continuous signature,” Candidate's Dissertation, Physical-Mathematical Sciences, Kishinev (1983).
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Balakovo, Saratovskii Region. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 28, No. 5, pp. 167–177, September–October, 1987.
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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
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DOI: https://doi.org/10.1007/BF00969330