# Prove that this set is open/closed

I have been recently studying topology and it's kind of difficult for me to use the theory in some tasks.I am not sure how to prove that this set is open/closed: $$A=\{(x,y,z) \in \Bbb R^3\mid 0\le x\le 1,\:0\le y\le 1,\:0\le z\le 1\}$$ I know that I have to use a ball and prove something of a kind that for every $x$ in $A$ there must exist an $r>0$ such that the ball with that kind of radius is a subset of $A$ but I am not really sure how to do that.Could someone give me a hand?

To be open, you need an open neighborhood around every point in set. In $R^3$ you can use open balls.
Take $(0,0,0)$ and any ball around it. Is it fully inside the $A$?
If it is $B((0,0,0), \varepsilon)$, then is $(-\frac{\varepsilon}{2},-\frac{\varepsilon}{2},-\frac{\varepsilon}{2}) \in A$?
To be closed, you either look at $A^C$, or you find the limit of every converging sequence, or you find every boundary point and check whether it is in $A$.