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)



Absolute $ C\sp{\ast} $-embedding of extremally disconnected spaces

Author: Alan Dow
Journal: Proc. Amer. Math. Soc. 81 (1981), 636-640
MSC: Primary 54C45; Secondary 54G05
MathSciNet review: 601745
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An extremally disconnected space $ X$ is $ {C^*}$-embedded in each extremally disconnected space in which it is embedded iff $ X$ is weakly Lindelöf or almost compact.

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

  • [A] C. E. Aull, Absolute $ {C^*}$-embedding of $ P$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 26 (1978), 831-836. MR 518988 (80a:54022)
  • [BS] B. Balcar and P. Simon, Convergent nets in the spaces of uniform ultrafilters, (preprint) 1978.
  • [CHN] W. W. Comfort, N. Hindman and S. Negrepontis, $ F'$-spaces and their product with $ P$-spaces, Pacific J. Math. 28 (1969), 489-502. MR 0242106 (39:3440)
  • [E] B. A. Efimov, Extremally disconnected spaces and absolutes, Trans. Moscow Math. Soc. 23 (1970), 243-285. MR 0418016 (54:6060)
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [I] J. R. Isbell, Zero-dimensional spaces, Tôhoku Math. J. 7 (1955), 7-8. MR 0086285 (19:156f)
  • [W] R. C. Walker, The Stone-Ĉech compactification, Springer-Verlag, Berlin and New York, 1974. MR 0380698 (52:1595)
  • [Wo] R. G. Woods, A survey of absolutes of topological spaces, Top. Structures 2, Math. Centre Tracts, no. 116, 1979, pp. 323-362. MR 565852 (81d:54019)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C45, 54G05

Retrieve articles in all journals with MSC: 54C45, 54G05

Additional Information

Keywords: Extremally disconnected, $ P$-set, the absolute
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society