Sober space
= Sober space
{wiki}
= Sober topological space
{synonym}
A <topological space> is sober when every nonempty <irreducible closed subset> is the closure of a unique point. Every <Hausdorff space> is sober. In contrast, an infinite set with the <cofinite topology> has the whole space irreducible and closed, while every singleton is closed, so it is not sober.