Connectedness of cone superefficient point sets in locally convex topological vector spaces (Q5925730)

For the superefficient point set \(SE(A,K)\) (Borwein/Zhung) in locally convex topological vector spaces it is shown: 1. \(SE(A,K) = \cup_{f \in \operatorname {int} K^*} \{ y \in A: f(y)= \operatorname {inf} \{ f(x): x \in A \} \}\) when \(A\) is \(K\)-convex, 2. \( SE(A,K)\) is connected when \(A\) is \(K\)-convex and weakly compact.