A new cardinal invariant related to adding real functions


Francis Jordan

Real Anal. Exchange 25(2) (1999-2000), 753-770.

Let F be a subset of RR. The additivity of F, shortly add(F), is the minimum cardinality of a subfamily G of RR with the property that h+G is a subset of F for no h in RR. In this paper we consider the notion of super-additivity which we will denote by add*. If F is a subset of RR, then add*(F) is the minimum cardinality of a family of functions G with the property that for any subset H of RR if |H| is less then add(F), then there is a g in G such that g+H is a subset of F. We calculate the super-additivities of the families of Darboux-like functions and their complements.

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Last modified December 6, 2000.