Transversals for strongly almost disjoint families
Paul J. Szeptycki · Proceedings of the American Mathematical Society · 2007
For a family of sets A A , and a set X X , X X is said to be a transversal of A A if X ⊆ ⋃ A X\subseteq \bigcup A and | a ∩ X | = 1 |a\cap X|=1 for each a ∈ A a\in A . X X is said to be a Bernstein set for A A if ∅ ≠ a ∩ X ≠ a \emptyset ot =a\cap X ot =a for each a ∈ A a\in A . Erdős and Hajnal first studied when an almost disjoint family admits a set such as a transversal or Bernstein set. In this note we introduce the following notion: a family of sets A A is said to admit a σ \sigma -transversal if A A can be written as A = ⋃