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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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)$.


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  • [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 0236880 (38 #5174)
  • [2] R. Engelking, Outline of general topology, Translated from the Polish by K. Sieklucki, North-Holland Publishing Co., Amsterdam; PWN-Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. MR 0230273 (37 #5836)
  • [3] 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 (22 #6994)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0292032-4
PII: S 0002-9939(1972)0292032-4
Keywords: Stone-Čech compactification, Hewitt realcompactification, extensions, $ C(X)$, $ {C^\ast}(X)$
Article copyright: © Copyright 1972 American Mathematical Society