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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, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
  • [2] V. I. Malykhin, Sequential bicompacta: Čech-Stone extensions and $ \pi $-points, Moscow Univ. Math. Bull. 30 (1975), 18-23.
  • [3] Roy C. Olson, Bi-quotient maps, countably bi-sequential spaces, and related topics, General Topology and Appl. 4 (1974), 1–28. MR 0365463

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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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