Additive selections of additive set-valued functions


Kazimierz Nikodim




Assume that $X$ and $Y$ are vector spaces, $K$ is a cone in $X$ and $F\colon K\to2^Y\backslash\{\emptyset\}$ is an additive set-valued function. We prove that if for some $x_0\in riK$ the set $F(x_0)$ has an extremal point, then there exists an additive selection of $F$.