Abstract:An elementary construction for an abundance of vector topologies $\xi $ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )'$ separates points of $E$ from zero is given.
Keywords: Hahn-Banach extension property, topological vector space
AMS Subject Classification: 46A22