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duality theorem |
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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. Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content. |
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