Convergence of time scales

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The set of time scales is the hyperspace $\mathrm{CL}(\mathbb{R})$. There are three popular topologies on hyperspaces: the induced topology by the Hausdorff metric, the Vietoris topology, and the Fell topology.

Which topology should be used on $\mathrm{CL}(\mathbb{R})$?

Let $\{\mathbb{T}_n\}_{n=0}^{\infty}$ be a countable sequence of time scales.