Polar set

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 ${\displaystyle (X,Y)}$ the polar set or polar of a subset ${\displaystyle A}$ of ${\displaystyle X}$ is a set ${\displaystyle A^{\circ }}$ in ${\displaystyle Y}$ defined as

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