An extremally disconnected first countable collectionwise Hausdorff space must be discrete.
2.
An extremally disconnected space that is also Boolean algebras, the Stonean spaces correspond to the complete Boolean algebras.
3.
It follows from this result that no infinite ?-adic Hausdorff space can be an extremally disconnected space.
4.
As topological spaces, all the ordinals are extremally disconnected in general ( there are open sets, for example the even numbers from ?, whose closure is not open ).
5.
In particular, for metric spaces, the property of being extremally disconnected ( the closure of every open set is open ) is equivalent to the property of being discrete ( every set is open ).
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