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Dual system

In mathematics, a dual system, dual pair or a duality over a field K {\displaystyle \mathbb {K} } is a triple ( X , Y , b ) {\displaystyle (X,Y,b)} consisting of two vector spaces, X {\displaystyle X} and Y {\displaystyle Y} , over K {\displaystyle \mathbb {K} } and a non-degenerate bilinear map b : X × Y → K {\displaystyle b:X\times Y\to \mathbb {K} } .

Weak topology, Definition, notation, and conventions & Overview