Unavoidable subprojections in union-closed set systems of infinite breadth. (May 2021) - Choi, Yemon; Ghandehari, Mahya; Pham, Hung Le
Abstract: We consider union-closed set systems with infinite breadth, focusing on three particular configurations T max ( E ), T min ( E ) and T ort ( E ) . 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.