Difference between revisions of "Convergence of time scales"
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==Which topology should be used on $\mathrm{CL}(\mathbb{R})$?== | ==Which topology should be used on $\mathrm{CL}(\mathbb{R})$?== | ||
| − | + | <strong>Example:</strong> Consider the sequence $\mathbb{T}_n = [0,n]$ of time scales. As $n$ approaches $\infty$ one would expect that the time scales to converge to the set $[0,\infty) \subset \mathbb{R}$. This does not occur, because we can compute | |
=References= | =References= | ||
Revision as of 20:37, 28 August 2014
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 $\mathrm{CL}(\mathbb{R})$?
Example: Consider the sequence $\mathbb{T}_n = [0,n]$ of time scales. As $n$ approaches $\infty$ one would expect that the time scales to converge to the set $[0,\infty) \subset \mathbb{R}$. This does not occur, because we can compute
References
<bibtex>@inproceedings{MR2547668,
title="The Fell topology on the space of time scales for dynamic equations",
author="Oberste-Vorth, Ralph W.",
booktitle="Advances in Dynamical Systems and Applications 2008",
}
</bibtex>
