Absolute $C^{\ast }$-embedding of extremally disconnected spaces
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- Proc. Amer. Math. Soc. 81 (1981), 636-640 Request permission
Abstract:
An extremally disconnected space $X$ is ${C^*}$-embedded in each extremally disconnected space in which it is embedded iff $X$ is weakly Lindelöf or almost compact.References
- Charles E. Aull, Absolute $C^{\ast }$-embedding of $P$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), no. 9-10, 831–836 (English, with Russian summary). MR 518988 B. Balcar and P. Simon, Convergent nets in the spaces of uniform ultrafilters, (preprint) 1978.
- W. W. Comfort, Neil Hindman, and S. Negrepontis, $F^{\prime }$-spaces and their product with $P$-spaces, Pacific J. Math. 28 (1969), 489–502. MR 242106
- B. A. Efimov, Extremally disconnected bicompacta and absolutes (on the occasion of the one hundredth anniversary of the birth of Felix Hausdorff), Trudy Moskov. Mat. Obšč. 23 (1970), 235–276 (Russian). MR 0418016
- 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
- J. R. Isbell, Zero-dimensional spaces, Tohoku Math. J. (2) 7 (1955), 1–8. MR 86285, DOI 10.2748/tmj/1178245102
- Russell C. Walker, The Stone-Čech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York-Berlin, 1974. MR 0380698
- R. Grant Woods, A survey of absolutes of topological spaces, Topological structures, II (Proc. Sympos. Topology and Geom., Amsterdam, 1978) Math. Centre Tracts, vol. 116, Math. Centrum, Amsterdam, 1979, pp. 323–362. MR 565852
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 636-640
- MSC: Primary 54C45; Secondary 54G05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0601745-9
- MathSciNet review: 601745