Every open subset of $\mathbb{R}$ can be expressed uniquely as a disjoint union of open intervals. Does this generalize to $\mathbb{R}^n$?

Every open subset of $\mathbb{R}$ can be expressed uniquely as a disjoint
union of open intervals. Does this generalize to $\mathbb{R}^n$?

I know that every open subset of $\mathbb{R}$ can be expressed uniquely as
a disjoint union of open intervals. Further, only countably many intervals
feature in any such decomposition.
Supposing we replace $\mathbb{R}$ with $\mathbb{R}^n$, and 'open
intervals' with 'open connected subsets,' does the above result still
hold?