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$ \beta (X)$ can be Fréchet

Author: Andrew J. Berner
Journal: Proc. Amer. Math. Soc. 80 (1980), 367-373
MSC: Primary 54D35; Secondary 54D55
MathSciNet review: 577776
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Abstract: A class of spaces is defined which share many properties of Gillman and Jerison's space $ \psi $. These spaces are used to generalize a theorem of Malykhin, showing that certain one point compactifications are Stone-Čech compactifications. This is used to construct a space whose Stone-Čech compactification is a Fréchet space (under a set theoretic assumption which follows, for example, from the continuum hypothesis).

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

  • [1] Leonard Gillman and Meyer Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 0116199 (22:6994)
  • [2] V. I. Malykhin, Sequential bicompacta: Čech-Stone extensions and $ \pi $-points, Moscow Univ. Math. Bull. 30 (1975), 18-23.
  • [3] R. C. Olson, Biquotient maps, countably bi-sequential spaces and related topics, General Topology and Appl. 4 (1974), 1-28. MR 0365463 (51:1715)

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Keywords: Fréchet space, Stone-Čech compactification, maximal almost disjoint families, pseudocompact, dense conditionally compact subset
Article copyright: © Copyright 1980 American Mathematical Society

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