I came across this definition
Let $U\subset S\subset C$. We say that $U$ is relatively open in $S$ if for every $z_0 \in U$, there is $r > 0$ such that $$D(z_0 ;r)\cap S\subset U$$:
Now the author doesnt specify if the subset symbol means that you do not count the trivial subsets ( the empty set and the set itself).
So then i came across another definition.
Definition :A set $S \subset C$ is called connected if the only relatively open and closed sets in S are the empty set and S.
Then i thought take the union of 3 disconnected open balls in C call it $K$.I know this set is disconnected so i want to prove it by the definition above.All i have to do is a find a relatively open closed subset in it except the trivials.SO there must be a closed subset call it $L$ of this set that is relatively open in it Because it is not connected.This means that for every $z_0$ in this closed set there exist an $r>0$ such that if i take the r-ball $\cap K\subset L$ .
Now i am trying to find a pictorial way for it.I drew 3 open circles.And i try to find a closed subset that for any element in it the $r$-ball is inside the closed set.there is no problem for the elements inside the closed set.But at the boundary of my closed subset cant find an $r$-ball without containing some elements that belong to $K$ and not in my closed set so the ball cant be a subset of my of my closed set.