# Vector space

1. Dec 5, 2007

### ercagpince

1. The problem statement, all variables and given/known data
Do functions that vanish at the end points x=0 and x=L form a vector space ? How about periodic functions obeying f(L)=f(0)? How about functions that obey f(0)=4 ?
If the functions do not qualify , list the things that go wrong .

2. Relevant equations
All axioms defining the vector space .

3. The attempt at a solution
I tried to sketch some functions collapsed on point x=L and x=0 and superposed them . But , I don't know how to make a pointwise addition of 2 functions which I don't know the explicit forms .
I guess functions mentioned on the problem are violating the closure feature of a vector space.

I got really confused