Dense extremally disconnected subspaces
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- by A. Dow and J. van Mill PDF
- Proc. Amer. Math. Soc. 121 (1994), 931-936 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 931-936
- MSC: Primary 54G05; Secondary 54A35
- DOI: https://doi.org/10.1090/S0002-9939-1994-1246523-4
- MathSciNet review: 1246523