Sober T0 space

Statement
A topological space $$X$$ is termed a sober T0 space if it is both a sober space and a Kolmogorov space (T0 space). Explicitly:


 * It is sober: the only irreducible closed subsets of $$X$$ are closures of singleton subsets.
 * It is T0: for any two distinct points $$x,y \in X$$, we can find either an open subset containing $$x$$ and not $$y$$, or an open subset containing $$y$$ and not $$x$$.