Standard coordinates
From Maths
Revision as of 22:32, 9 April 2015 by Alec (Talk | contribs) (Created page with " ==Definition== For each {{M|n\in\mathbb{N} }} the Euclidean space {{M|\mathbb{R}^n}} is a manifold}} with the Smooth structure|smooth structu...")
Definition
For each n∈N the Euclidean space Rn is a smooth n-manifold with the smooth structure determined by the atlas determined by the single chart (Rn,IdRn)
This structure is the standard smooth structure on Rn and the resulting coordinate map yields the (so called) standard coordinates[1]
The only standard thing is that we deal with them already
References
- Jump up ↑ Introduction to smooth manifolds - John M Lee - Second Edition