Large basis dimension and metrizability
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- by Gary Gruenhage PDF
- Proc. Amer. Math. Soc. 54 (1976), 397-400 Request permission
Abstract:
In this paper it is proved that if $X$ is a regular Lindelöf space having finite large basis dimension, then $X$ is metrizable if and only if it is a $\Sigma$-space or a $w\Delta$-space.References
- A. V. Arhangel′skiĭ, $k$-dimensional metrizable spaces, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1962 (1962), no. 2, 3–6 (Russian, with English summary). MR 0143178
- A. Arhangel′skiĭ, Ranks of systems of sets and dimensionality of spaces, Fund. Math. 52 (1963), 257–275 (Russian). MR 152989
- A. V. Arhangel′skiĭ and V. V. Filippov, Spaces with bases of finite rank, Mat. Sb. (N.S.) 87(129) (1972), 147–158 (Russian). MR 0296881
- Carlos J. R. Borges, On metrizability of topological spaces, Canadian J. Math. 20 (1968), 795–804. MR 231355, DOI 10.4153/CJM-1968-078-1
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606 A. F. Monna, Remarques sur les métriques non-archimédiennes. I, II, Nederl. Akad. Wetensch. Proc. 53, 470-481, 625-637 = Indag. Math. 12(1950), 122-133, 179-191. MR 12, 41, 1002.
- Keiô Nagami, $\Sigma$-spaces, Fund. Math. 65 (1969), 169–192. MR 257963, DOI 10.4064/fm-65-2-169-192
- Peter J. Nyikos, Some surprising base properties in topology, Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), Academic Press, New York, 1975, pp. 427–450. MR 0367940 P. J. Nyikos and H. C. Reichel, On the structure of zero-dimensional spaces, Indag. Math. (to appear).
- Takanori Shiraki, $M$-spaces, their generalization and metrization theorems, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A 11 (1971), 57–67. MR 305365
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 397-400
- DOI: https://doi.org/10.1090/S0002-9939-1976-0394586-X
- MathSciNet review: 0394586