Is it possible to partition a topological space into nonempty disjoint closed subsets?

Question

Let $X$ be a topological space containing at least 2 elements. Is it true, in general, that there exist 2 disjoint closed nonempty subsets $A$ and $B$ of $X$, such that $$X = A \cup B?$$ Is it false, in general?

Answer 1

It is true if and only if $X$ is not connected.