I'm reading into an introductory book on manifolds (Tu) and they start out by showing vectors are isomorphic to derivations at a point. They go on to introduce covectors, k-tensors, and then I've just gotten to the point where they introduce the "d" operator which constructs a 1-form from a continuous function. It seems like vectors in R^n can be interpreted isomorphically as points in R^n (though I haven't tried to prove it.) This suggests that there is really no difference between functions (R^n --> R) and covectors, and so I feel a little bit confused or unsure about things. Is this just a fluke for this specific type of k-tensor (i.e., the covector) or am I interpreting things incorrectly?