Wikipedia: Tangent space

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Changed: 1,2c1,5

The easiest definition of the tangent space is as the dual
of the cotangent space.

The easiest definition of the tangent space at a point of a C^∞ manifold is as the dual
of the cotangent space at that point.

We need the geometrical definition here for C^k manifolds, and the definition via derivations. Vector fields and tangent bundles should be mentioned.

The easiest definition of the tangent space at a point of a C^∞ manifold is as the dual of the cotangent space at that point.

We need the geometrical definition here for C^k manifolds, and the definition via derivations. Vector fields and tangent bundles should be mentioned.