This is a preview of subscription content, log in via an institution to check access.
Literature Cited
A. V. Arkhangel'skii, “Any topological group is a quotient group of a zero-dimensional topological group,” Dokl. Akad. Nauk SSSR,285, No. 5, 1037–1040 (1981).
A. V. Arkhangel'skii, “Classes of topological groups,” Usp. Mat. Nauk,36, No. 3, 127–146 (1981).
V. K. Bel'nov, “On the dimension of free topological groups,” in: Abstracts, IVth Tiraspol Symp. General Topology and Applications, 1979 [in Russian], Shtiintsa, Kishinev (1979), pp. 14–15.
M. M. Choban, “On some questions of the theory of topological groups,” in: General Algebra and Discrete Geometry [in Russian], Shtiintsa, Kishinev (1980), pp. 120–135.
M. G. Tkachenko, “On zero-dimensional topological groups,” in: Proc. Leningrad International Topology Conf. [in Russian], Nauka, Leningrad (1983), pp. 113–118.
V. G. Pestov, “Homomorphisms of topological groups do not factorize with respect to weight and dimension,” Mat. Zametki,41, No. 2, 217–225 (1987).
E. C. Nummela, “Uniform free topological groups and Samuel compactifications,” Topology Appl.,13, No. 1, 77–83 (1982).
V. G. Pestov, “Neighborhoods of the identity in free topological groups,” Vestn. Mosk. Gos. Univ., Ser. 1, Mat. Mekh., No. 3, 8–10 (1985).
O. V. Sipacheva, “Zero-dimensionality and completeness in free topological groups,” Serdika,15, 119–154 (1989).
A. V. Arkhangel'skii, “On maps connected with topological groups,” Dokl. Akad. Nauk SSSR,181, No. 6, 1303–1306 (1968).
D. B. Shakhmatov, “Factorization theorems for topological groups,” in: Scientific-Research Seminar on General Topology. Sessions of Spring Semester, 1985/86 School Year, Vestn. Mosk. Gos. Univ., Ser. 1, Mat. Mekh., No. 4, 112–114-(1988).
M. G. Tkačenko, “On topologies of free groups,” Czech. Mat. J.,34, 541–551 (1984).
I. I. Guran, “On topological groups close to being eventually compact,” Dokl. Akad. Nauk SSSR,256, No. 6, 1035–1037 (1981).
V. V. Uspenskii, “A topological group generated by a Lindelöf Σ-space possesses the Suslin property,” Dokl. Akad. Nauk SSSR,265, No. 4, 823–826 (1982).
M. Katetov, “A theorem on the Lebesgue dimension,” Časopis Pro Pěst. Mat. Fys.,75, No. 2, 79–87 (1950).
Yu. M. Smirnov, “On the dimension of proximity spaces,” Mat. Sb.,38, 283–302 (1956).
M. G. Tkačenko, “Factorization theorems for topological groups and their applications,” Topology Appl.,38, No. 1, 21–37 (1991).
P. S. Aleksandrov and B. A. Pasynkov, Introduction to Dimension Theory [in Russian], Nauka, Moscow (1973).
R. Engelking, Dimension Theory, PWN, Warsaw (1978).
M. G. Tkachenko, “Generalization of the Comfort-Ross theorem,” Ukr. Mat. Zh.,41, No. 3, 377–382 (1989).
D. A. Raikov, “On completion of topological groups,” Izv. Akad. Nauk SSSR,10, 513–528 (1946).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 151–159, May–June, 1991.
Rights and permissions
About this article
Cite this article
Tkachenko, M.G. Zero-dimensional groups and factorization of homomorphisms with respect to weight and dimensionality. Sib Math J 32, 477–484 (1991). https://doi.org/10.1007/BF00970486
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970486