Polar set

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See also polar set (potential theory).

In functional analysis and related areas of mathematics the polar set of a given subset of a vector space is a certain set in the dual space.

Given a dual pair the polar set or polar of a subset of is a set in defined as

The bipolar of a subset of is the polar of . It is denoted and is a set in .




In geometry, the polar set may also refer to a duality between points and planes. In particular, the polar set of a point , given by the set of points satisfying is its polar hyperplane, and the dual relationship for a hyperplane yields its pole.

See also


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Discussion of Polar Sets in Potential Theory: Ransford, Thomas: Potential Theory in the Complex Plane, London Mathematical Society Student Texts 28, CUP, 1995, pp. 55-58.