Polar 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)](/Images/godic/202502/03/f00acce613318349cb04ab296486fc114555.png")
the polar set or polar of a subset ![A](/Images/godic/202502/03/7fc56270e7a70fa81a5935b72eacbe294555.png")
of ![X](/Images/godic/202502/03/02129bb861061d1a052c592e2dc6b3834555.png")
is a set ![A^\circ](/Images/godic/202502/03/ef407b0dc3570b1431210308412d820d4555.png")
in ![Y](/Images/godic/202502/03/57cec4137b614c87cb4e24a3d003a3e04555.png")
defined as
The bipolar of a subset of is the polar of . It is denoted ![A^{\circ\circ}](/Images/godic/202502/03/f5b342664aca96a6bbdb6ccc4987607a4555.png")
and is a set in .