On solidness of polar cones

We investigate the properties of cones whose polars are solid in different polar topologies. By a standard duality argument, we obtain a number of nec essary and sufficient conditions for closed convex cones to be solid in var ious locally convex spaces. From this, we can deduce easily the extensions of previous related results. Furthermore, we construct a class of closed co nvex cones in some Banach spaces, which are not solid but whose polars sati sfy the angle property. This solves the Han conjecture in the negative.