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)

 
 

 

Horrors of topology without $ {\rm AC}$: a nonnormal orderable space


Author: Eric K. van Douwen
Journal: Proc. Amer. Math. Soc. 95 (1985), 101-105
MSC: Primary 03E25; Secondary 03E35, 03E65, 04A25, 54D15, 54F05, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1985-0796455-5
MathSciNet review: 796455
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the absence of AC there can be a space which is not normal, yet which is orderable and is the topological sum of countably many compact countable metrizable spaces.


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

  • [B] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, R. I., 1967; reprinted with corrections, 1979. MR 0227053 (37:2638)
  • [J$ _{1}$] T. J. Jech, The axiom of choice, North-Holland, Amsterdam, 1973.
  • [J$ _{2}$] -, Set theory, Academic Press, New York, 1978. MR 506523 (80a:03062)
  • [HLZ] R. W. Heath, D. J. Lutzer and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481-493. MR 0372826 (51:9030)
  • [L] H. Lächli, Auswahl Axiom in der Algebra, Comment. Math. Helv. 37 (1963), 1-18.
  • [Lu] D. J. Lutzer, Ordered topological spaces, Surveys in General Topology (G. M. Reed, ed.), Academic Press, New York, 1980, pp. 247-295. MR 564104 (81d:54026)
  • [M] M. J. Mansfield, Some generalizations of full normality, Trans. Amer. Math. Soc. 86 (1957), 489-505. MR 0093753 (20:273)
  • [S] L. A. Steen, A direct proof that a linearly ordered space is collectionwise normal, Proc. Amer. Math. Soc. 24 (1970), 727-728. MR 0257985 (41:2634)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E25, 03E35, 03E65, 04A25, 54D15, 54F05, 54G20

Retrieve articles in all journals with MSC: 03E25, 03E35, 03E65, 04A25, 54D15, 54F05, 54G20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0796455-5
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society