# Questions tagged [duality-theorems]

For question about the concept of dual, either in the sense of vector spaces, topological group or dual problems.

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### How does Liu intend his readers to compute $H^0(X,\Omega^1_{X/k})$ of this scheme?

In the chapter on duality theory in Liu's Algebraic Geometry and Arithmetic Curves, there is the following exercise. I'm having trouble seeing how one can apply the duality theory developed in Liu to ...
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### Dual and completion of metric spaces

Say we have a metric space $(M,d)$, and we want to complete it in the following sense: Definition: A completion of $(M,d)$ is a complete metric space $(\widetilde{M},d')$ together with a Lipschitz ...
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### The principle of duality for sets

The Wikipedia article on the algebra of sets briefly mentions the following: These are examples of an extremely important and powerful property of set algebra, namely, the principle of duality for ...
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### Finding the dual of this primal LP.

I am going over sample questions from a sample exam, and I got stuck on the following question. I need to determine the dual of this LP: $min: c^Tx + d^Tu \\ s.t: Ax + Du = b\\ x \ge 0$ $A$ is an $m$...
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### Motivation to understand double dual space

I am helping my brother with Linear Algebra. I am not able to motivate him to understand what double dual space is. Is there a nice way of explaining the concept? Thanks for your advices, examples ...
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Let $M$ be an $n$-dimensional compact and oriented manifold. Then one can define the intersection pairing $H_k(M,\mathbb Z) \times H_{n-k}(M,\mathbb Z) \to \mathbb Z$. One possible formulation of the ...