Prove $B(x,\delta)$ is open. 
Prove $B(x,\delta)$ is open.

What this question is asking me to prove...? I don't understand nor have a clue to approach the question...

To prove that $B(x,\delta)$ you should show that for every $y\in B(x,\delta)$ we find $r>0$ such that
$$B(y,r)\subset B(x,\delta)$$
Hint Draw a picture to see how to find $r$.
