ON CLOSEDNESS IN THE L-TOPOLOGY OF T.V.S.
Yungyen Chiang, Y. S. Wang · Taiwanese Journal of Mathematics · 2006
Let X and Y be Hausdorff and locally convex topological vector spaces. In this paper, we prove that a convex subset of X is closed if and only if it is closed in the topology on X induced by the set of continuous linear mappings from X into Y . As applications, some existence results for vector equilibrium problems and vector variational inequalities associated with discontinuous mappings are given.