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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# No difference between covectors and functions?

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