Dual topology | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-06

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Dual_topology


00:00:57 1 Definition
00:03:54 2 Properties
00:04:18 3 Characterization of dual topologies
00:05:17 3.1 Mackey–Arens theorem



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SUMMARY
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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.