Unavoidable subprojections in union-closed set systems of infinite breadth

摘要

We consider union-closed set systems with infinite breadth, focusing on three particular configurations T-max(epsilon), T-min(epsilon) and T-ort(epsilon). We show that these three configurations are not isolated examples; in any given union-closed set system of infinite breadth, at least one of these three configurations will occur as a subprojection. This characterizes those union-closed set systems which have infinite breadth, and is the first general structural result for such set systems. (C) 2021 Elsevier Ltd. All rights reserved.