Abstract
Symmetrizable spaces are characterized and an example of a regular final compact symmetrizable space without a countable network is constructed (assuming the continuum hypothesis).
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A. V. Arkhangel'skii, “Mappings and spaces,” Usp. Matem. Nauk,21, No. 4, 133–184 (1966).
M. M. Choban, “Mappings of metric spaces,” Dokl. Akad. Nauk SSSR,184, 1298–1300 (1969).
Ya. Kofner, “A new class of spaces and some problems in the theory of symmetrizability,” Dokl. Akad. Nauk SSSR,187, 270–273 (1969).
R. W. Heath, “On open mappings and certain spaces satisfying the first countable axiom,” Fund. Math.,57, 91–96 (1965).
R. W. Heath, “Arc-wise connectedness in semimetric spaces,” Pacific J. Math.,12, 1301–1319 (1962).
S. I. Nedev, “o-Metrizable spaces,” Trudy Mosk. Matem. O-va,24, 201–236 (1971).
K. Kuratovskii, Topology [in Russian], Vols. 1, 2, Moscow (1966).
E. S. Berney, “A regular Lindelöf semimetric space which has no countable network,” Proc. Amer. Math. Soc.,26, 361–364 (1970).
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 577–582, November, 1972.
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Velichko, N.V. Symmetrizable spaces. Mathematical Notes of the Academy of Sciences of the USSR 12, 784–786 (1972). https://doi.org/10.1007/BF01099065
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DOI: https://doi.org/10.1007/BF01099065