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A note on identifications of metric spaces


Author: Frank Siwiec
Journal: Proc. Amer. Math. Soc. 57 (1976), 340-344
MSC: Primary 54E20; Secondary 54C10
DOI: https://doi.org/10.1090/S0002-9939-1976-0413053-8
MathSciNet review: 0413053
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Abstract: A space $ X$ is said to be $ \sigma MK$ provided that $ X$ has a countable closed cover $ \mathcal{C}$ of metrizable subspaces such that if $ K$ is a compact subset of $ X$, there is a $ C \in \mathcal{C}$ for which $ K \subset C$. A Hausdorff space is $ \sigma MK$ and Fréchet if and only if it is representable as a closed image of a metric space obtained by identifying a discrete collection of closed sets with hemicompact boundaries to points.


References [Enhancements On Off] (What's this?)

  • [1] R. F. Arens, A topology for spaces of transformations, Ann. of Math. (2) 47 (1946), 480-495. MR 8, 165. MR 0017525 (8:165e)
  • [2] S. P. Franklin, Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115. MR 31 #5184. MR 0180954 (31:5184)
  • [3] K. Morita, On decomposition spaces of locally compact spaces, Proc. Japan Acad. 32 (1956), 544-548. MR 19, 49. MR 0085495 (19:49d)
  • [4] K. Morita and S.Hanai, Closed mappings and metric spaces, Proc. Japan Acad. 32 (1956), 10-14. MR 19, 299. MR 0087077 (19:299a)
  • [5] F. Siwiec, Countable spaces having exactly one nonisolated point. I, Proc. Amer. Math. Soc. 57 (1976), 345-350. MR 0413064 (54:1185)
  • [6] -, Generalizations of the first axiom of countability, Rocky Mountain J. Math. 5 (1975), 1-60. MR 0358699 (50:11158)
  • [7] A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690-700. MR 19, 299. MR 0087078 (19:299b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0413053-8
Keywords: $ \sigma MK$ space, closed image of a metric space
Article copyright: © Copyright 1976 American Mathematical Society

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