= Solution
{c}
The set $A$ is <disconnected space> if it has a <separation of a topological space>: two nonempty disjoint subsets $U,V$ open in $A$ with $A=U\cup V$. Each is then also closed in $A$, being the other's complement.
The set $A$ is <connected> if no such <separation of a topological space> exists. Equivalently its only subsets that are both open and closed are $\varnothing$ and $A$. A <separation of a topological space> uses openness in $A$ rather than necessarily in the entire <complex plane>.
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