Since this relation holds at each point p, the dx | p provide a basis for the cotangent space at each p and the bases dx | p and ∂/∂ x | p are dual to each other, d x μ μ | p ( ∂ ∂ ∂ ∂ x ν ν | p ) = δ δ ν ν μ μ . at each p. Furthermore, one has α α ⊗ ⊗ β β ( a , b ) = α α ( a ) β β ( b ) for general one-forms on a tangent space α, β and general tangent vectors a, b. (This can be taken as a definition, but may also be proved in a more general setting.)