Compactification by the topologist’s sine curve
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- by Ronnie Levy PDF
- Proc. Amer. Math. Soc. 63 (1977), 324-326 Request permission
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
- David P. Bellamy, A non-metric indecomposable continuum, Duke Math. J. 38 (1971), 15–20. MR 271911
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199, DOI 10.1007/978-1-4615-7819-2
- J. W. Rogers Jr., On compactifications with continua as remainders, Fund. Math. 70 (1971), no. 1, 7–11. MR 283763, DOI 10.4064/fm-70-1-7-11
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 324-326
- MSC: Primary 54D35
- DOI: https://doi.org/10.1090/S0002-9939-1977-0438294-6
- MathSciNet review: 0438294