I am trying to get a better understanding of the weak topology. I have read that the strong and weak topologies are equivalent in finite dimensions, and may be different in infinite dimensions. By the strong topology, I mean the topology due to the norm, and by the weak topology I mean the weakest topology such that every bounded linear functional is continuous.
So does anyone know of explicit examples that shows how these topologies are equivalent in finite dimensions, but may be different in infinite dimensions?