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## Main Question or Discussion Point

So i was considering minkowski space which is a 4-d manifold, why is that we use the tangent and cotangent space, to construct tensors on the space?

The definition of a manifold says that the space is locally homeomorphic to Euclidean space. So is the tangent space and cotangent space defined at each point used as a substitute for this homeomorphic euclidean space?

The definition of a manifold says that the space is locally homeomorphic to Euclidean space. So is the tangent space and cotangent space defined at each point used as a substitute for this homeomorphic euclidean space?