A new cardinal invariant related to adding real functions. (Q1852330)

The author considers a notion of super-addivity (\(A^{*}\)). If \(F\subset \mathbb{R}^{\mathbb{R}}\), then \(A^{*}(F)\) is the minimum cardinality of a family of functions \(G\) with the property that for any \(H\subset \mathbb{R}^{\mathbb{R}}\) if \(| H| <A(F)\) (where \(A(F)\) denotes an addivity of \(F\)), there is \(g\in G\) such that \(g+H\subset F\). The main results of this paper are connected with the super-additivities for Darboux-like classes of functions.