In differential geometry, one can attach to every point *x* of a smooth (or differentiable) manifold a vector space called the **cotangent space** at *x*. Typically, the cotangent space is defined as the dual space of the tangent space at *x*, although there are more direct definitions (see below). The elements of the cotangent space are called **cotangent vectors** or **tangent covectors**.

Read more about Cotangent Space: Properties, The Differential of A Function, The Pullback of A Smooth Map, Exterior Powers

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### Famous quotes containing the word space:

“For good teaching rests neither in accumulating a shelfful of knowledge nor in developing a repertoire of skills. In the end, good teaching lies in a willingness to attend and care for what happens in our students, ourselves, and the *space* between us. Good teaching is a certain kind of stance, I think. It is a stance of receptivity, of attunement, of listening.”

—Laurent A. Daloz (20th century)