Dense extremally disconnected subspaces

Dow, A.; van Mill, J.

doi:10.1090/S0002-9939-1994-1246523-4

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.

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Cardinality of

complete Boolean algebras

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