Unavoidable subprojections in union-closed set systems of infinite breadth

We consider union-closed set systems with infinite breadth, focusing on three particular configurations ${\mathcal T}_{\rm max}(E)$, min}(E)$ and ort}(E)$. show that these are not isolated examples; in any given system of at least one will occur as a subprojection. This characterizes those which have is the first general structural result for such systems.