Mackey topology

In functional analysis and related areas of mathematics, the Mackey topology, named after George Mackey, is the finest topology for a topological vector space which still preserves the continuous dual. In other words the Mackey topology does not make linear functions continuous which were discontinuous in the default topology. A topological vector space (TVS) is called a Mackey space if its topology is the same as the Mackey topology.
The Mackey topology is the opposite of the weak topology, which is the coarsest topology on a topological vector space which preserves the continuity of all linear functions in the continuous dual.
The Mackey–Arens theorem states that all possible dual topologies are finer than the weak topology and coarser than the Mackey topology.
Definition.
When is endowed with the Mackey topology then it will be denoted by or simply or if no ambiguity can arise. 
The definition of the Mackey topology for a topological vector space (TVS) is a specialization of the above definition of the Mackey topology of a pairing. 
If is a TVS with continuous dual space , then the evaluation map on is called the canonical pairing. 
That is, the Mackey topology is the polar topology on obtained by using the set of all weak*-compact disks in . 
When is endowed with the Mackey topology then it will be denoted by or simply if no ambiguity can arise. 
Applications.
The Mackey topology has an application in economies with infinitely many commodities.