In functional analysis and related areas of mathematics a **dual topology** is a locally convex topology on a dual pair, two vector spaces with a bilinear form defined on them, so that one vector space becomes the continuous dual of the other space.

The different dual topologies for a given dual pair are characterized by the Mackey–Arens theorem. All locally convex topologies with their continuous dual are trivially a dual pair and the locally convex topology is a dual topology.

Several topological properties depend only on the dual pair and not on the chosen dual topology and thus it is often possible to substitute a complicated dual topology by a simpler one.

Read more about Dual Topology: Definition, Properties, Characterization of Dual Topologies

### Other articles related to "dual topology, dual, topology":

**Dual Topology**- Characterization of Dual Topologies - Mackey–Arens Theorem

... Given a

**dual**pair with a locally convex space and its continuous

**dual**then is a

**dual topology**on if and only if it is a

**topology**of uniform convergence on a family of absolutely convex and weakly ...

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