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A topological space is disconnected space if it can be written as the union of two disjoint nonempty open subsets. Such a pair is a separation of a topological space. Each of the subsets is also closed, and conversely a nontrivial subset that is both open and closed gives a separation of a topological space with its complement.

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.