Classifying almost-disjoint families with applications toβN − N

Multiple gaps

“…The concept traces back to [11]. Completely separable almost disjoint families exist under the assumption that a = c [14] or s = ω 1 [4, Corollary 2.8].…”

A countable Fréchet–Urysohn space of uncountable character

“…This notion was first introduced by S. Hechler in [7] for the special case when the family A is maximal.…”

History of the Continuum in the 20th Century

“…For example, Hechler [1971] raises the question of whether there is a completely separable maximal almost disjoint family. An almost disjoint family A is said to be completely separable if for every X ⊆ N either X is almost contained in the union of finitely many members of A or there is A ∈ A such that X ⊇ A.…”