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Proceedings of the American Mathematical Society

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Stratifiable $ \sigma $-discrete spaces are $ M\sb{1}$

Author: Gary Gruenhage
Journal: Proc. Amer. Math. Soc. 72 (1978), 189-190
MSC: Primary 54E20
MathSciNet review: 0500850
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Abstract: It is shown that stratifiable $ \sigma $-discrete spaces are $ {M_1}$. A corollary is that scattered stratifiable spaces are $ {M_1}$.

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

  • [1] J. G. Ceder, Some generalizations of metric spaces, Pacific J. Math. 11 (1961), 105-126. MR 0131860 (24:A1707)
  • [2] G. Gruenhage, Stratifiable spaces are $ {M_2}$, Topology Proceedings 1 (1976), 221-226. MR 0448307 (56:6614)
  • [3] R. W. Heath, D. J. Lutzer and P. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481-493. MR 0372826 (51:9030)
  • [4] H. Junnila, Neighbornets (to appear). MR 0482677 (58:2734)
  • [5] P. J. Nyikos, Covering properties on $ \sigma $-scattered spaces, Topology Proceedings (to appear).

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Keywords: Stratifiable, $ {M_1}$-space, monotonically normal
Article copyright: © Copyright 1978 American Mathematical Society

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