= Solution
{c}
The topology on $A$ is the <subspace topology> inherited from the <complex plane>. A subset $B$ is open in $A$ if $B=A\cap U$ for some <open subset> $U\subseteq\mathbb C$. Equivalently, every $b\in B$ has a radius $\epsilon>0$ such that $A\cap\{z:|z-b|<\epsilon\}\subseteq B$.
A subset $B$ is closed in $A$ if $A\setminus B$ is open in $A$, equivalently if $B=A\cap F$ for a <closed subset> $F$ of the <complex plane>. These are relative properties: the same subset need not be open or closed in the ambient plane.
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