query of M.J.Frade

In response to Maria Joao Frade <mjf@di.uminho.pt>, I believe the following is true: Let $X$ be an infinite space with the cofinite topology, i.e., $U\subseteq X$ is open if and only if $U$ is empty or the complement of $U$ is finite. This space is ${\bf T}_0$---${\bf T}_1$, even---but it is not sober, since $X$ is irreducible closed, but $X$ is not the closure of any point. (You can make $X$ into a coherent space by adding a generic point for $X$.) $\Omega(X)$ is coherent. It is isomorphic to ${\rm Idl}(L)$, where $L$ is the lattice of all $\{0,1}\}$-valued functions on $X$ that are $1$ except at finitely many points. J. Madden