Cardinal invariants connected with adding real functions


Francis Jordan

Real Anal. Exchange 22(2), 696--713.

In this paper we consider a cardinal invarient related to adding real valued functions defined on the real line. Let F be a such a family, we consider the smallest cardinality of a family G of functions such that h+G has non-empty intersection with F for every function h. We note that this cardinal is the additivity, a cardinal invarient previously studied, of the compliment of F. Thus, we calculate the additivities of the compliments of various families of functions including the darboux, almost continuous, extendable, and perfect road functions. We briefly consider the relationship between the additivity of a family and its compliment.

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