A compactification of locally compact spaces
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- by F. W. Lozier PDF
- Proc. Amer. Math. Soc. 31 (1972), 577-579 Request permission
Abstract:
Every locally compact space $X$ has its topology determined by its 1-1 compact images and hence has a compactification $\xi X$ obtained as the closure of the natural embedding of $X$ in the product of those images, just as the Stone-Čech compactification $\beta X$ can be obtained by embedding $X$ in a product of intervals. The obvious question is whether $\xi X = \beta X$. In this paper we prove that $\xi X = \beta X$ if $X$ either is $0$-dimensional or contains an arc, and give an example in which $\xi X \ne \beta X$.References
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- 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
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 577-579
- DOI: https://doi.org/10.1090/S0002-9939-1972-0286072-9
- MathSciNet review: 0286072