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Proceedings of the American Mathematical Society

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

 

 

There can be $ C\sp *$-embedded dense proper subspaces in $ \beta\omega-\omega$


Authors: Eric K. van Douwen, Kenneth Kunen and Jan van Mill
Journal: Proc. Amer. Math. Soc. 105 (1989), 462-470
MSC: Primary 54D35; Secondary 03E35, 54A35
DOI: https://doi.org/10.1090/S0002-9939-1989-0977925-7
MathSciNet review: 977925
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Abstract: Fine and Gillman have shown that CH implies that if $ X$ is a dense proper subspace of $ {\omega ^ * } = \beta \omega - \omega $, then $ \beta X \ne {\omega ^ * }$. Here it is shown to be consistent with $ {\text{MA + c = }}{\omega _2}$ that for every $ p \in {\omega ^ * }$ we have $ \beta ({\omega ^ * } - \{ p\} ) = {\omega ^ * }$ and also that $ {\omega ^ * }$ has a dense subspace $ X$ with dense complement such that $ \beta X = {\omega ^ * }$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0977925-7
Keywords: Space of ultrafilters, Čech-Stone compactification, $ {P_c}$-set, $ (\kappa ,\lambda )$-gap
Article copyright: © Copyright 1989 American Mathematical Society