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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
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 0236880,
  • [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
  • [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

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Keywords: Stone-Čech compactification, Hewitt realcompactification, extensions, $ C(X)$, $ {C^\ast}(X)$
Article copyright: © Copyright 1972 American Mathematical Society

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