Topology of Mrówka-Isbell spaces

Abstract

An infinite family A of infinite subsets of the natural numbers, ω, is almost disjoint (AD) if the intersection of any two distinct elements of A is finite. It is maximal almost disjoint (MAD) if given an infinite X ⊂ ω there is an A ε A such that │ A ∩ X │ = ω, in other words, if the family A is not included in any larger almost disjoint family.