Hello,

Could anybody please help me to solve some problems:

1. Prove that closure of opened ball with radius r in normed linear space is equal to closed ball with radius r, r>0.

2. Show that interior of the closed ball with radius r in normed linear space is equal to opened ball with radius r, r>0.

3. Show that 1., 2. doen't apply to metric space.

4. Prove that closure of space Y is closed vector subspace of X, if Y is vector subspace of normed linear space X.

5. Show that closure of K is closed convex subspace of X, if K is convex subspace of normed linear space X.

Thank you in advance.