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The Stone-Čech compactification, the Stone-Čech remainder, and the regular Wallman property


Author: Takashi Kimura
Journal: Proc. Amer. Math. Soc. 99 (1987), 193-198
MSC: Primary 54D35; Secondary 54D40
DOI: https://doi.org/10.1090/S0002-9939-1987-0866452-1
MathSciNet review: 866452
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Abstract: In this paper, the following are proved: (1) the Stone-Čech compactification of a metrizable space is regular Wallman, (2) if the Stone-Čech compactification of a locally compact space whose pseudocompact closed subsets are compact is regular Wallman, then the Stone-Čech remainder is also regular Wallman. Consequently, the Stone-Čech remainder of a locally compact metrizable space is regular Wallman.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0866452-1
Keywords: Regular Wallman, Stone-Čech compactification, Stone-Čech remainder
Article copyright: © Copyright 1987 American Mathematical Society

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