Dense Extremally Disconnected Subspaces
Copyright policy )Dense Extremally Disconnected Subspaces
We prove that every compact Basically Disconnected space of π \pi -weight ω 1 {\omega _1} has a dense Extremally Disconnected subspace. In Boolean algebraic terms: every σ \sigma -complete Boolean algebra B with density ω 1 {\omega _1} carries an ultrafilter which generates an ultrafilter in the completion of B. The statement that every compact Basically Disconnected space of weight c \mathfrak {c} has a dense Extremally Disconnected subspace is shown to be equivalent to CH.
Consistency and independence results in general topology, extremally disconnected subspace, basically disconnected space, Boolean algebra, Extremally disconnected spaces, \(F\)-spaces, etc., remote point
Consistency and independence results in general topology, extremally disconnected subspace, basically disconnected space, Boolean algebra, Extremally disconnected spaces, \(F\)-spaces, etc., remote point
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