Cardinal invariants concerning extendable and peripherally continuous functions (Q1374520)

Let \(\mathcal F\) and \(F\) be families of real functions defined on the line. Denote by \(A(\mathcal F)\) the minimal cardinal \(m\) such that if card\((F)\geq m\) and \(g\) is a real function then \(f+g\notin \mathcal F\), for some \(f\in F\). Let \(\mathfrak c\) be the cardinality of the real numbers. The authors prove that, e.g., \(A(\mathcal F)={\mathfrak c}^+\), if \(\mathcal F\) is the class of extendable functions, or functions of perfect road, respectively, and \(A(\mathcal F)=2^{\mathfrak c}\), if \(\mathcal F\) is the class of peripherally continuous functions. They also consider a multiplicative analogue of the problem.