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 that we will investigate: 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.
