数学上，极端不连通空间是一种拓扑空间，适合以下的等价定义：

一个极端不连通的紧致豪斯多夫空间，有时会称为Stonean空间。（注意与Stone空间的分别：Stone空间是完全不连通的紧致豪斯多夫空间。）Andrew Gleason的一条定理指紧致豪斯多夫空间范畴的投射对象正是极端不连通的紧致豪斯多夫空间。就如Stone空间和布尔代数之间有对偶性，Stonean空间和完全布尔代数范畴也有对偶性。

In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. (The term "extremally disconnected" is usual, even though the word "extremally" does not appear in most dictionaries.)