MAD Families of Projections on l² and Real-Valued Functions on Omega

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Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [omega]ᵒmega and omegaᵒmega have been studied for quite some time. In particular, the cardinal invariants a and aₑ, defined to be the minimum cardinality of a maximal infinite almost disjoint family of [omega]ᵒmega and omegaᵒmega respectively, are known to be consistently less than continuum. Here we examine analogs for functions in Rᵒmega and projections on l², showing that they too can be consistently less than continuum.