duality theorem (redirected from Duality (mathematics))

duality theorem [dü′al·əd·ē ‚thir·əm]

(mathematics)

A theorem which asserts that for a givenn-dimensional space, the (n-p) dimensional homology group is isomorphic to ap-dimensional cohomology group for eachp= 0, …,n, provided certain conditions are met.

LetGbe either a compact group or a discrete group, letXbe its character group, and letG′be the character group ofX; then there is an isomorphism ofGontoG′so that the groupsGandG′may be identified.

If either of two dual linear-programming problems has a solution, then so does the other.