Difference between revisions of "Convergence of time scales"
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(Created page with "The set of time scales is the [http://dualaud.net/hyperspacewiki/index.php/Hyperspace hyperspace] $\mathrm{CL}(\mathbb{R})$. There are three popular [http://d...") |
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| − | The set of [[time_scale | time scales]] is the [http://dualaud.net/hyperspacewiki/index.php/Hyperspace hyperspace] $\mathrm{CL}(\mathbb{R})$. There are three popular [http://dualaud.net/hyperspacewiki/index.php/Topological_space topologies] on hyperspaces | + | The set of [[time_scale | time scales]] is the [http://dualaud.net/hyperspacewiki/index.php/Hyperspace hyperspace] $\mathrm{CL}(\mathbb{R})$. There are three popular [http://dualaud.net/hyperspacewiki/index.php/Topological_space topologies] on hyperspaces: the induced topology by the [http://dualaud.net/hyperspacewiki/index.php/Hausdorff_metric Hausdorff metric], the [http://dualaud.net/hyperspacewiki/index.php/Vietoris_topology Vietoris topology], and the [http://dualaud.net/hyperspacewiki/index.php?title=Fell_topology Fell topology]. |
==Which topology should be used on $\mathrm{CL}(\mathbb{R})$?== | ==Which topology should be used on $\mathrm{CL}(\mathbb{R})$?== | ||
Let $\{\mathbb{T}_n\}_{n=0}^{\infty}$ be a countable sequence of time scales. | Let $\{\mathbb{T}_n\}_{n=0}^{\infty}$ be a countable sequence of time scales. | ||
Revision as of 19:36, 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 $\mathrm{CL}(\mathbb{R})$?
Let $\{\mathbb{T}_n\}_{n=0}^{\infty}$ be a countable sequence of time scales.
