Strong topology (polar topology)
- Strong topology (polar topology)
In functional analysis and related areas of mathematics the strong topology is the finest polar topology, the topology with the most open sets, on a dual pair. The coarsest polar topology is called weak topology.
Definition
Given a dual pair the strong topology on is the polar topology defined by using the family of all sets in where the polar set in is absorbent.
Examples
* Given a normed vector space and its continuous dual then -topology on is identical to the topology induced by the operator norm. Conversely -topology on is identical to the topology induced by the norm.
Properties
* In barrelled spaces the strong topology is identical to the Mackey topology.
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