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• If two charts are smoothly compatible with an atlas then they are smothly compatible with each other
  ...oth manifold]] from a [[topological manifold]]. We may speak of a (smooth) atlas on a space that is simply locally euclidean, it need not be a full on [[top *# {{M|(V,\psi)}} is [[smoothly compatible with the atlas]] {{M|\mathcal{A} }} and
  6 KB (1,182 words) - 13:38, 1 April 2017

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• Chart
  ...on map]] for moving between charts, and [[Smoothly compatible charts]] for the smooth form. * {{M|U}} is called the ''coordinate domain'' or ''coordinate neighbourhood'' of each of its points
  2 KB (322 words) - 06:32, 7 April 2015
• Smoothly compatible charts
  ...t|charts]], {{M|(U,\varphi)}} and {{M|(V,\psi)}} are said to be ''smoothly compatible''<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> This is vital to define [[Smooth atlas|smooth atlases]]
  727 B (101 words) - 12:27, 12 November 2015
• Smooth atlas
  '''Note:''' a smooth atlas is a special kind of [[Atlas]] An [[Atlas|atlas]] {{M|\mathcal{A} }} is called a ''smooth atlas''<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref>
  2 KB (242 words) - 12:27, 12 November 2015
• Smooth manifold
  ===Smoothly compatible charts=== ...arts|smoothly compatible charts]]) - Two charts are smoothly compatible if the intersections of their domains is empty, or there is a [[Diffeomorphism|dif
  3 KB (413 words) - 21:09, 12 April 2015
• Smooth structure
  ...as, or a smooth atlas which is not properly contained in any larger smooth atlas ...atlas. However as this example shows there are many smooth atlases giving the same "smooth structure"
  2 KB (246 words) - 07:10, 7 April 2015
• Smooth function
  ** That is to say {{M|f\circ\varphi^{-1} }} is [[Smooth|smooth]] in the usual sense - of having continuous partial derivatives of all orders. Theorem: Any other chart in {{M|(M,\mathcal{A})}} will also satisfy the definition of {{M|f}} being smooth
  3 KB (560 words) - 16:16, 14 April 2015
• Motivation for smooth structures
  ...function {{M|f:M\rightarrow\mathbb{R} }} which is continuous. Notice that the notion of continuity on such a map is easy! However suppose we want to diff ...hbb{R}^n}}", {{M|\psi}} and {{M|\varphi}} are [[chart|charts]] from some [[atlas]].
  2 KB (414 words) - 12:26, 12 November 2015
• If two charts are smoothly compatible with an atlas then they are smothly compatible with each other
  ...oth manifold]] from a [[topological manifold]]. We may speak of a (smooth) atlas on a space that is simply locally euclidean, it need not be a full on [[top *# {{M|(V,\psi)}} is [[smoothly compatible with the atlas]] {{M|\mathcal{A} }} and
  6 KB (1,182 words) - 13:38, 1 April 2017