The transversal property implies Property B

Families close to disjoint ones

“…Any of these definitions implies the next (the only non-trivial implication is Def3~Def. 4, which is the main result of [10]). However; it is easy to see that Def.…”

Comparing almost-disjoint families

“…d has a transversal -a one-to-one choice function. That the transversal property really implies property B, at least for families of infinite sets, is proved in [1]. The strongest property to date gained from the Miller condition is the following: d is essentially disjoint, i.e.…”