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)



Spaces for which the generalized Cantor space $ 2\sp{J}$ is a remainder

Author: Yusuf Ünlü
Journal: Proc. Amer. Math. Soc. 86 (1982), 673-678
MSC: Primary 54D35; Secondary 54D40
MathSciNet review: 674104
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a locally compact noncompact space, $ m$ be an infinite cardinal and $ \vert J \vert = m$. Let $ F(X)$ be the algebra of continuous functions from $ X$ into $ {\mathbf{R}}$ which have finite range outside of an open set with compact closure and let $ I(X) = \{ g \in F(X):g$ vanishes outside of an open set with compact closure}. Conditions on $ R(X) = F(X)/I(X)$ and internal conditions are obtained which characterize when $ X$ has $ {2^J}$ as a remainder.

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

  • [E] B. A. Efimov, Extremally disconnected compact spaces and absolutes, Trans. Moscow Math. Soc. 23 (1970), 243-282.
  • [GJ] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [HM] J. Hatzenbuhler and A. Mattson, Spaces for which all compact metric spaces are remainders, Proc. Amer. Math. Soc. 82 (1981), 478-480. MR 612744 (82j:54037)
  • [M] K. D. Magill, The lattice of compactifications of a locally compact space, Proc. London Math. Soc. 18 (1968), 231-244. MR 0229209 (37:4783)
  • [R] M. C. Rayburn, On the Stoilov-Kerékjartó compactification, J. London Math. Soc. 6 (1973), 193-196. MR 0322809 (48:1170)
  • [W] S. Willard, General topology, Addison-Wesley, London, 1970. MR 0264581 (41:9173)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D35, 54D40

Retrieve articles in all journals with MSC: 54D35, 54D40

Additional Information

Keywords: Compactification, structure space, Freudenthal compactification, Cantor space
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society