= Solution
Every point belongs to its component, so the components cover $X$; by part (ii) they are pairwise disjoint, and by part (iii) they are nonempty open <interval>[intervals]. Each contains a <rational number>. Fix an enumeration of $\mathbb Q$ and choose the first rational belonging to each component. Distinct components receive distinct rationals, giving an <injection> from the component family into a <countable set>. Therefore
$$
\boxed{X\text{ is a countable union of pairwise disjoint open intervals}.}
$$
The empty <open set> is represented by the empty union.
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