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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dense extremally disconnected subspaces


Authors: A. Dow and J. van Mill
Journal: Proc. Amer. Math. Soc. 121 (1994), 931-936
MSC: Primary 54G05; Secondary 54A35
MathSciNet review: 1246523
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Abstract: We prove that every compact Basically Disconnected space of $ \pi $-weight $ {\omega _1}$ has a dense Extremally Disconnected subspace. In Boolean algebraic terms: every $ \sigma $-complete Boolean algebra B with density $ {\omega _1}$ carries an ultrafilter which generates an ultrafilter in the completion of B. The statement that every compact Basically Disconnected space of weight $ \mathfrak{c}$ has a dense Extremally Disconnected subspace is shown to be equivalent to CH.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1246523-4
PII: S 0002-9939(1994)1246523-4
Keywords: Extremally and Basically Disconnected, remote points, Boolean algebra
Article copyright: © Copyright 1994 American Mathematical Society