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)



Compactification by the topologist's sine curve

Author: Ronnie Levy
Journal: Proc. Amer. Math. Soc. 63 (1977), 324-326
MSC: Primary 54D35
MathSciNet review: 0438294
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Using a compactification of the nonnegative reals whose remainder is the topologist's sine curve, results about growths of Stone-Čech compactifications are proved. For example, it is proved that if $ \beta X$ contains a nonconstant continuous image of a compact connected LOTS, then the image is contained in $ \upsilon X$. This extends a result of Peter Nyikos.

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

  • [1] D.P. Bellamy, A non-metric indecomposable continuum, Duke Math. J. 38 (1971), 15-10. MR 42 # 6792. MR 0271911 (42:6792)
  • [2] J. Dugundji, Topology, Allyn and Bacon, Boston; 1966. MR33 # 1824. MR 0193606 (33:1824)
  • [3] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, N.J., 1960. MR22 # 6994. MR 0116199 (22:6994)
  • [4] J.W. Rogers, Jr., On compactifications with continua as remainders, Fund. Math. 70 (1971), no. 1, 7-11. MR 44 # 993. MR 0283763 (44:993)

Similar Articles

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

Retrieve articles in all journals with MSC: 54D35

Additional Information

Keywords: T-path, Stone-Čech compactification
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society