On the graph of a quasi-additive function
The author considers quasi-additive functions, i.e. functions \(f:X\to {\mathbb{R}}\) satisfying the condition \(| f(x+y)-f(x)-f(y)| \leq \epsilon \min \{| f(x+y)|,| f(x)+f(y)| \},\) x,y\(\in X\), with an \(0\leq \epsilon <1\) [cf. \textit{J. Tabor}, ibid. 35, 164-185 (1988; Zbl 0652.39013)]. It is shown that if X is a locally convex space and \(f:X\to {\mathbb{R}}\) is a discontinuous quasi-additive function, then the graph of f is dense in \(X\times {\mathbb{R}}\).
scientific article; zbMATH DE number 4159320