Problem: Let and . Assuming is continuous, prove that is exact.
is a vector space denoting the set of 1-forms on .
is the length of the vector , so .
So this is how I tried to approach the problem. I need to find a function, say , such that .
+ + ... +
Then I want to find , but I don't know how to take the derivative of since I don't know what is - and what I'm taking the derivative with respect to each time is within .
You can probably tell I'm not familiar with proofs dealing with sum notation. Any tips?