tangent space

Noun

 * 1)  An n-dimensional vector space that represents the set of all vectors tangent to given n-dimensional  M at point x.

Usage notes
Typically denoted TxM, although the manifold may be omitted if understood.

More strictly, for any smooth curve in M passing through x, its derivative at x is a vector in TxM.

Translations

 * Italian: spazio tangente
 * Japanese: 接空間