In functional and convex analysis, and related disciplines of mathematics, the polar set A ∘ {\displaystyle A^{\circ }} is a special convex set associated to any subset A {\displaystyle A} of a vector space X , {\displaystyle X,} lying in the dual space X ′ . {\displaystyle X^{\prime }.} The bipolar of a subset is the polar of A ∘ , {\displaystyle A^{\circ },} but lies in X {\displaystyle X} (not X ′ ′ {\displaystyle X^{\prime \prime }} ).
In functional and convex analysis, and related disciplines of mathematics, the polar set A ∘ {\displaystyle A^{\circ }} is a special convex set associated to any subset A {\displaystyle A} of a vector space X , {\displaystyle X,} lying in the dual space X ′ . {\displaystyle X^{\prime }.} The bipolar of a subset is the polar of A ∘ , {\displaystyle A^{\circ },} but lies in X {\displaystyle X} (not X ′ ′ {\displaystyle X^{\prime \prime }} ).
Source: Wikipedia "Polar set" · CC BY-SA 4.0
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