On closedness in the \(\mathcal L\)-topology of T.V.S. (Q2493615)

Let \(X\) and \(Y\) be Hausdorff locally convex topological vector spaces and let \(L(X,Y)\) denote the set of linear continuous functions from \(X\) to \(Y\). The authors compare closedness with respect to the original topology of \(X\) and closedness with respect to the topology induced on \(X\) by the family \(L(X,Y)\). Their study is motivated by the analysis of a certain vector equilibrium problem. As introduction to this topic the reader may consider the paper by \textit{Y. Chiang} and \textit{J. C. Yao} [J. Optimization Theory Appl. 116, No. 2, 251--264 (2003; Zbl 1030.49006)].