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

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.

References

compact spaces

Charles M. Biles, Wallman-type compactifications, Proc. Amer. Math. Soc. 25 (1970), 363–368. MR 263029, DOI 10.1090/S0002-9939-1970-0263029-3
Richard E. Chandler, Hausdorff compactifications, Lecture Notes in Pure and Applied Mathematics, Vol. 23, Marcel Dekker, Inc., New York-Basel, 1976. MR 0515002
W. W. Comfort, On the Hewitt realcompactification of a product space, Trans. Amer. Math. Soc. 131 (1968), 107–118. MR 222846, DOI 10.1090/S0002-9947-1968-0222846-1
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
Orrin Frink, Compactifications and semi-normal spaces, Amer. J. Math. 86 (1964), 602–607. MR 166755, DOI 10.2307/2373025
J. van Mill, Compactifications in which the collection of multiple points is Lindelöf semi-stratifiable, Nederl. Akad. Wetensch. Proc. Ser. A 79=Indag. Math. 38 (1976), no. 4, 349–356. MR 0442888, DOI 10.1016/1385-7258(76)90075-5
Arvind K. Misra, Some regular Wallman $\beta X$, Nederl. Akad. Wetensch. Proc. Ser. A 76=Indag. Math. 35 (1973), 237–242. MR 0324653, DOI 10.1016/1385-7258(73)90009-7
R. C. Solomon, A Hausdorff compactification that is not regular Wallman, General Topology and Appl. 7 (1977), no. 1, 59–63. MR 433390, DOI 10.1016/0016-660X(77)90007-1
E. F. Steiner, Wallman spaces and compactifications, Fund. Math. 61 (1967/68), 295–304. MR 222849, DOI 10.4064/fm-61-3-295-304

Solution of a basic problem on compactifications of Wallman type

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R. Grant Woods, Co-absolutes of remainders of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545–560. MR 307179, DOI 10.2140/pjm.1971.37.545