Sums of Darboux-like functions from Rn to Rm


Francis Jordan

Real Anal. Exchange 24(2) (1998-99), 729-759.

The additivity A(F) of a family F of functions from R to R is the minimum cardinality of a family G of functions from R to R with the property that f+G is a subset of F for no f:R-->R. The values of A have been calculated for many families of Darboux-like functions from R to R. We extend these results to include some families of Darboux-like functions in from Rn to R. To do this we must define a new cardinal function called generalized additivity which is much more flexible than A.

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