A topological space is called zero-dimensional if it has a base consisting of clopen sets. Now, let $U_1$ and $U_2$ be two open subsets of a topological zero-dimensional topological space $X$. As my previous question, I am looking for an equivalent condition for $\overline{U_1}\subseteq U_2$, where $\overline{U_1}$ is the closure of $U_1$ in $X$.
Closure of open sets in zero-dimensional topological space
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