Recent content by benjamin111

I'm sorry all. I meant that the space is [-1,1] rather than [0,1]. Sorry again and do appreciate any help.

Homework Statement Let Ce([0,1], R) be the set of even functions in C([0,1], R), show that Ce is closed and not dense in C. Homework Equations The Attempt at a Solution I think I can solve this if I can show that even functions converge to even functions, but I can't quite...

I guess I don't quite see how that parallels this sum of closed sets. Isn't it more like just dividing closed sets over and over? If you could run me through how to interpret the function in terms of the problem I'm looking at I'd be most appreciative

Sorry, I thought i had included that A and B have to be closed but I forgot to write that in...

We have two closed sets A,B in R^n. Does A+B= {x+y | x is an element of A, y is an element of B} have to be closed? I know that both the union and intersection of two closed sets have to be closed. I'm guessing from the question that the answer is no, but I've been playing around with different...

Homework Statement My textbook states that the inverse of a bijection is also a bijection and is unique. I understand how to show that the inverse would be a bijection and intuitively I understand that it would be unique, but I'm not sure how to show that part. Homework Equations...