I have this set of complex numbers: $\{ 1-i , 2-i , 3-i \}$, and another set $$B:= \{ w \in \Bbb{C} \mid 0 \leq \mathrm{Re}(w)\leq 4 \land -2 < \mathrm{Im}(w)\leq0 \} \setminus \{ a+bi \in \Bbb{C} \mid 2<a<5 \land -1\leq b\leq2\}.$$
I need to check for every $z \in \{ 1-i , 2-i , 3-i \}$ whether the set $B$ is a neighborhood of $z$.
What I did is this:
$B=\{(0-i),(0+0i),(1-i),(1+0i),(2-i),(2+0i)\}$, and now I say: for $z=1-i$,$z=2-i$ the set $B$ can be neighborhood of them, since $z+\epsilon/2$ and $z-\epsilon/2$ still live in $B$.
Can you please correct me? Thanks for any guidance!
It would be helpful to start with a visualization (but pay attention to which portions of the common blue region are open vs closed based on your inequalities given):