$\beta (X)$ can be Fréchet
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- by Andrew J. Berner
- Proc. Amer. Math. Soc. 80 (1980), 367-373
- DOI: https://doi.org/10.1090/S0002-9939-1980-0577776-3
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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
- 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, DOI 10.1007/978-1-4615-7819-2 V. I. Malykhin, Sequential bicompacta: Čech-Stone extensions and $\pi$-points, Moscow Univ. Math. Bull. 30 (1975), 18-23.
- Roy C. Olson, Bi-quotient maps, countably bi-sequential spaces, and related topics, General Topology and Appl. 4 (1974), 1–28. MR 365463, DOI 10.1016/0016-660X(74)90002-6
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 367-373
- MSC: Primary 54D35; Secondary 54D55
- DOI: https://doi.org/10.1090/S0002-9939-1980-0577776-3
- MathSciNet review: 577776