Polar set

（重定向自Bipolar set）

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

The bipolar of a subset $A$ of $X$ is the polar of $A^\circ$ . It is denoted $A^{\circ\circ}$ and is a set in $X$ .

单词	Bipolar set
释义	Bipolar set 英语百科 Polar set （重定向自Bipolar set） 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 $(X,Y)$ the polar set or polar of a subset $A$ of $X$ is a set $A^\circ$ in $Y$ defined as The bipolar of a subset $A$ of $X$ is the polar of $A^\circ$ . It is denoted $A^{\circ\circ}$ and is a set in $X$ .
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