Difference between revisions of "Standard coordinates"
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Latest revision as of 22:32, 9 April 2015
Definition
For each [ilmath]n\in\mathbb{N} [/ilmath] the Euclidean space [ilmath]\mathbb{R}^n[/ilmath] is a smooth [ilmath]n[/ilmath]-manifold with the smooth structure determined by the atlas determined by the single chart [ilmath](\mathbb{R}^n,\text{Id}_{\mathbb{R}^n})[/ilmath]
This structure is the standard smooth structure on [ilmath]\mathbb{R}^n[/ilmath] and the resulting coordinate map yields the (so called) standard coordinates[1]
The only standard thing is that we deal with them already
References
- ↑ Introduction to smooth manifolds - John M Lee - Second Edition
