  We consider the duality between General Relativity and the theory of Einstein
algebras, in the extended setting where one permits non-Hausdorff manifolds. We
show that the duality breaks down, and then go on to discuss a sense in which
general relativity, formulated using non-Hausdorff manifolds, exhibits excess
structure when compared to Einstein algebras. We discuss how these results bear
on a class of algebraically-motivated deflationist views about spacetime
ontology. We conclude with a conjecture concerning non-Hausdorff spacetimes
with no bifurcate curves.
