a space $X$ is said to be extremally disconnected if every open set has an open closure.
$X$ is basically disconnected if every cozero-set has an open closure.
hence any extremally disconnected space is basically disconnected. The converse fails.
1: Is every open subspace of an extermally disconnected space extermally disconnected? Is it true for basically disconnected?
2:In an extermally disconnected space, are any two disjoint zero-sets completely seperated?
( Or even in an bacically disconnected space, are any two disjoint cozero-sets completely seperated?)