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In this paper we prove that the Scott topology $\mathfrak S$ on a rootednon-metric tree $\mathcal T$ is strictly coarser than the weak tree topology.Moreover, for each $t\in \mathcal T$, we consider a natural order $\preceq_t$on $\mathcal T$ under which $t$ is the root of $\mathcal T$. Then the weak treetopology is generated by the union of the Scott topologies $\mathfrak S_t$associated to $\preceq_t$.

The Scott topology of a rooted non-metric tree