duality theorem

[dü′al·əd·ē ‚thir·əm] (mathematics) A theorem which asserts that for a given n-dimensional space, the (n-p) dimensional homology group is isomorphic to a p-dimensional cohomology group for each p = 0, …, n, provided certain conditions are met. Let G be either a compact group or a discrete group, let X be its character group, and let G′ be the character group of X ; then there is an isomorphism of G onto G′ so that the groups G and G′ may be identified. If either of two dual linear-programming problems has a solution, then so does the other.

单词	duality theorem
释义	duality theorem duality theorem [dü′al·əd·ē ‚thir·əm] (mathematics) A theorem which asserts that for a given n-dimensional space, the (n-p) dimensional homology group is isomorphic to a p-dimensional cohomology group for each p = 0, …, n, provided certain conditions are met. Let G be either a compact group or a discrete group, let X be its character group, and let G′ be the character group of X ; then there is an isomorphism of G onto G′ so that the groups G and G′ may be identified. If either of two dual linear-programming problems has a solution, then so does the other.
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