The polar topology originates from the $S$-topology and is used in duality pairs. Due to the connection between the original topology and the weak topology, we can rephrase the original topology in terms of the polar topology, i.e. the Mackey-Arens theorem. I want to know how the whole mechanism works and what other uses there are of the polar topology.

The polar topology originates from the $S$-topology and is used in duality pairs. Due to the connection between the original topology and the weak topology, we can rephrase the original topology in terms of the polar topology, i.e. the Mackey-Arens theorem. I want to know how the whole mechanism works (the advantage of using polar topology) and what other uses there are of the polar topology.

The polar topology originates from S-topology and is used in duality pair. Due to the connection between original topology and weak topology, we can rephrase the original topology by polar topology, i.e. Mackey-Arens theorem. I want to know how the whole mechanism works and what other use of polar topology? Thanks.

The polar topology originates from the $S$-topology and is used in duality pairs. Due to the connection between the original topology and the weak topology, we can rephrase the original topology in terms of the polar topology, i.e. the Mackey-Arens theorem. I want to know how the whole mechanism works and what other uses there are of the polar topology.