Abstract
In this paper for superparacompact complete metrizable spaces the Freudenthal’s theorem for compact irreducible standard polyhedric representation is generalized. Furthermore, for superparacompact metric spaces are reinforced: 1) the Morita’s theorem about universality of the product Q ∞ × B(τ) of Hilbert cube Q ∞ to generalized Baire space B(τ) of the weight τ in the space of all strongly metrizable spaces of weight ≤ τ; 2) the Nagata’s theorem about universality of the product Φn × B(τ) of universal n-dimensional compact Φn to B(τ) in the space of all strongly metrizable spaces ≤ τ and dimension dimX ≤ n.
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References
P. S. Aleksandrov and B. A. Pasynkov, Introduction to the theory of dimensionality (Nauka, Moscow, 1973).
D. K. Musaev, SiberianMath. Journal 46(4), 851 (2005).
D. K. Musaev, Reports of Uzbek Academy of Sciences 2, 5 (1983).
R. Engelking, General topology (Mir, Moscow, 1986).
H. Freudenthal, Compositio Mat. 4, 145 (1937).
D. L. Kelli, General topology (Nauka, Moscow, 1981).
D. K. Musaev, Reports of Uzbek Academy of Sciences 6, 5 (1983).
D. K. Musaev and B. A. Pasynkov About properties of compactness and completeness of topological spaces and continuous mappings (FAN, Tashkent, 1994).
B. A. Pasynkov, Reports of Academy of Sciences USSR 221(3), 543 (1975).
K. Morita, Math. Ann. 128(4), 350 (1954).
J. Nagata, Fundam. Math. 45(2), 143 (1958).
A. V. Arkhangelskiy and V. I. Ponomarev, Foundation of general topology in problems and exercises (Nauka, Moscow, 1974).
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Submitted by P.N. Ivanshin
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Musaev, D.K. On generalization of the Freudenthal’s theorem for compact irreducible standard polyhedric representation for superparacompact complete metrizable spaces. Lobachevskii J Math 32, 328–333 (2011). https://doi.org/10.1134/S1995080211040159
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DOI: https://doi.org/10.1134/S1995080211040159