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An alternative construction of $ \beta X$ and $ \upsilon X$


Author: Richard E. Chandler
Journal: Proc. Amer. Math. Soc. 32 (1972), 315-318
MSC: Primary 54D35
DOI: https://doi.org/10.1090/S0002-9939-1972-0292032-4
MathSciNet review: 0292032
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Abstract: A different construction of $ \beta X$ and $ \upsilon X$ is given emphasizing the extension property and the role played by $ C(X)$.


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

  • [1] W. W. Comfort, A theorem of Stone-Čech type, and a theorem of Tychonoff type, without the axiom of choice; and their realcompact analogues, Fund. Math. 63 (1968), 97-110. MR 38 #5174. MR 0236880 (38:5174)
  • [2] R. Engelking, Outline of general topology, PWN, Warsaw, 1965; English transl., North-Holland, Amsterdam; Interscience, New York, 1968. MR 36 #4508; MR 37 #5836. MR 0230273 (37:5836)
  • [3] L. Gillman and M. Jerison, Rings of continuous functions. University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #6994. MR 0116199 (22:6994)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292032-4
Keywords: Stone-Čech compactification, Hewitt realcompactification, extensions, $ C(X)$, $ {C^\ast}(X)$
Article copyright: © Copyright 1972 American Mathematical Society

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