Cotangent Space
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Definition*. (Tu11, pp. 34) The cotangent space to at , denoted by , is defined to be the dual space of the Euclidean tangent space .
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Definition*. (Tu11, pp. 34) The cotangent space to Rn at p, denoted by Tp∗(Rn), is defined to be the dual space (Tp(Rn))∨ of the Euclidean tangent space Tp(Rn).