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

Kimura, Takashi

doi:10.1090/S0002-9939-1987-0866452-1

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

Proc. Amer. Math. Soc. 99 (1987), 193-198

DOI: https://doi.org/10.1090/S0002-9939-1987-0866452-1

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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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