I often meet the question whether the (physical) space is 'covariant' or 'contravariant'. I once replied to that question with: Space is space. The COMPONENTS of a tensor are covariant/contravariant if the basis is CHOSEN TO BE contravariant/covariant. As far as I know tensors the 'covariance' or 'contravariance' of space (or tensor) itself is not even the question. The thing is that the professors were not satisfied with the answer. They said the space is contravariant. So, I am confused. As far as I know tensors, or better saying tensor components, the 'covariance' or 'contravariance' depends on the choice of basis, i.e. contravariant or covariant basis. In other words, tensor cannot be covariant or contravariant, it can only be represented in covariant or contravariant BASIS and therefore having contravaiant or covariant components. Does anyone have any ideas about that?