Loterre: Mathematics: polar set

mathematical analysis > functional analysis > polar set

geometry > convex analysis > polar set

algebra > linear algebra > vector space > topological vector space > polar set

polar set

In functional and convex analysis, and related disciplines of mathematics, the polar set ${\\displaystyle A^{\\circ }}$ is a special convex set associated to any subset ${\\displaystyle A}$ of a vector space ${\\displaystyle X,}$ lying in the dual space ${\\displaystyle X^{\\prime }.}$ The bipolar of a subset is the polar of ${\\displaystyle A^{\\circ },}$ but lies in ${\\displaystyle X}$ (not ${\\displaystyle X^{\\prime \\prime }}$ ).
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Polar_set)

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