1 Answers
In mathematics, an extremally disconnected space is a topological space in which the closure of every open set is open.
An extremally disconnected space that is also compact and Hausdorff is sometimes called a Stonean space. This is different from a Stone space, which is usually a totally disconnected compact Hausdorff space. In the duality between Stone spaces and Boolean algebras, the Stonean spaces correspond to the complete Boolean algebras.
An extremally disconnected first-countable collectionwise Hausdorff space must be discrete. In particular, for metric spaces, the property of being extremally disconnected is equivalent to the property of being discrete.
4 views
Answered