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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Normal spaces whose Stone-Čech remainders have countable tightness


Author: Jin Yuan Zhou
Journal: Proc. Amer. Math. Soc. 117 (1993), 1193-1194
MSC: Primary 54D40
MathSciNet review: 1132425
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Abstract: We prove, assuming PFA, that each normal space whose Stone-Čch remainder has countable tightness is ACRIN. A normal space $ X$ is called ACRIN if each of its regular images is normal. Fleissner and Levy proved that if $ X$ is normal and every countably compact subset of the Stone-Čech remainder $ \beta X\backslash X$ is closed in $ \beta X\backslash X$, then $ X$ is ACRIN. They asked if each normal space whose Stone-Čech remainder has countable tightness is ACRIN. Theorem $ 2$ gives the positive answer assuming the Proper Forcing Axiom.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1132425-X
Article copyright: © Copyright 1993 American Mathematical Society