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Is every compact Hausdorff space the filtered colimit of compact extremally disconnected spaces?

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  • $\begingroup$ Have you tried the bar resolution associated to the ultrafilter monad? $\endgroup$
    – André Henriques
    Commented Mar 27 at 13:02
  • $\begingroup$ @AndréHenriques No I haven't: I will take a look at this and report back. $\endgroup$
    – Peter Kropholler
    Commented Mar 27 at 14:33
  • $\begingroup$ @AndréHenriques You may well be right, but I have not figured out how to extract a filtered colimit from a resolution. $\endgroup$
    – Peter Kropholler
    Commented Mar 28 at 11:52
  • $\begingroup$ You're right: It's only sifted. Not filtered. $\endgroup$
    – André Henriques
    Commented Mar 29 at 22:46

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