Definition:Differential Form
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Definition
Let $X$ be a smooth manifold.
A p-form on $X$ is a function $\omega: T_x \left({X}\right)^p \to \R$ defined at each point of $X$ which takes $p$ vectors as inputs, and outputs a real number.
Here $T_x \left({X}\right)$ is the tangent space of $X$.
What has this to do with differentials? In other words: can the language of this be tightened up?
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