Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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


Author: Gary Gruenhage
Journal: Proc. Amer. Math. Soc. 72 (1978), 189-190
MSC: Primary 54E20
DOI: https://doi.org/10.1090/S0002-9939-1978-0500850-5
MathSciNet review: 0500850
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E20

Retrieve articles in all journals with MSC: 54E20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0500850-5
Keywords: Stratifiable, $ {M_1}$-space, monotonically normal
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society