A Note on Polar Topologies

Abstract

Let (E, E') be a dual pair and G be a collection of σ(E, E') bounded sets in E with the following properties:i)G contains all singletons.ii)If A, B are in G there is a C in G with A ∪B ⊆ C.iii)If A is in G then λ A ε G for any scaler λ.Then sets of the form the polar of Ai, form base of neighbourhoods in E' for the polar topology TG of G convergence.