Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces
Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces
Local convexity appears-by the Hahn-Banach theorem-as a sufficient condition for the (topological) dual of a topological vector space to separate points from closed subspaces.The aim in the present article is to obtain necessary conditions, in terms of local convexity, for the latter statement to hold for a metrizable topological vector …