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• Closure, interior and boundary
  ...e{A} }} ("overline" in LaTeX) is the set:<ref>Introduction to Topological Manifolds - John Lee</ref>
  1 KB (210 words) - 00:20, 9 March 2015
• Index of notation
  * Manifolds * Manifolds
  9 KB (1,490 words) - 06:13, 1 January 2017
• Tangent space
  ...ngent space to {{M|\mathbb{R}^n}} at {{M|p}}'''<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> is defined as follows: ...ngent space to {{M|\mathbb{R}^n}} at {{M|p}}'''<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> is defined as follows:
  6 KB (1,190 words) - 19:27, 14 April 2015
• Set of all derivations of a germ at a point
  ...o manifolds - Second Edition</ref><ref>John M Lee - Introduction to smooth manifolds - second edition</ref> denotes the set of all [[Derivation|derivations]] of {{Definition|Manifolds|Differential Geometry}}
  772 B (132 words) - 21:49, 13 April 2015
• Leibniz rule
  ...mooth Manifolds - Second Edition - John M Lee</ref><ref>An introduction to manifolds - Second Edition - Loring W. Tu</ref> if: {{Definition|Differential Geometry|Manifolds}}
  723 B (123 words) - 00:57, 5 April 2015
• Set of all derivations at a point
  ...s use <math>T_p(\mathbb{R}^n)</math><ref>Loring W. Tu - An introduction to manifolds - second edition</ref> to denote the [[Tangent space]] - while isomorphic t * [[Manifolds]]
  2 KB (291 words) - 21:51, 13 April 2015
• Germ
  {{Definition|Differential Geometry|Manifolds}}
  2 KB (285 words) - 01:36, 5 April 2015
• The set of all germs of smooth functions at a point
  ...manifolds - Second Edition - Loring W. Tu</ref><ref>Introduction to smooth manifolds - Second Edition - John M. Lee</ref> is the set of all [[Germ|germs]] of <m {{Definition|Differential Geometry|Manifolds}}
  794 B (140 words) - 01:50, 5 April 2015
• Derivation
  ...-linear and satisfies the following<ref name="ITSM">Introduction to Smooth Manifolds - John M. Lee - Second Edition - Springer GTM</ref>: {{Definition|Manifolds}}
  2 KB (325 words) - 18:08, 14 October 2015
• Smooth
  ...}} is also open, we say a function<ref>John M Lee - Introduction to smooth manifolds - Second Edition</ref> <math>F:U\rightarrow V</math> is '''smooth''', <math {{Definition|Differential Geometry|Manifolds}}
  870 B (148 words) - 06:38, 7 April 2015
• Smooth manifold
  '''Note: ''' It's worth looking at [[Motivation for smooth manifolds]] A ''smooth manifold'' is<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> a pair {{M|(M,\mathcal{A})}} where {{M|
  3 KB (413 words) - 21:09, 12 April 2015
• Smooth structure
  A smooth structure<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> is a '''maximally''' [[Smooth atlas|smo We wish to define "smooth" functions on manifolds, eg {{M|f:M\rightarrow\mathbb{R} }} is smooth if and only if {{M|f\circ\var
  2 KB (246 words) - 07:10, 7 April 2015
• Motivation for tangent space
  Using the notation of [[Motivation for smooth manifolds#Our charts|the charts for the smooth manifold of (upper quadrant) of the pl [[Category:Manifolds]]
  6 KB (975 words) - 00:18, 11 April 2015
• Smooth function
  ...ifold}}]], {{M|(M,\mathcal{A})}}, is a function<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> {{M|f:M\rightarrow\mathbb{R} }} that sa Without knowledge of [[Smooth manifold|smooth manifolds]] we may already define {{M|C^\infty(\mathbb{R}^n)}} - the set of all funct
  3 KB (560 words) - 16:16, 14 April 2015
• Motivation for tangent space definitions
  ...on for tangent space]] - that page talks about tangents, and going between manifolds. THIS page will talk about the reason for definitions. Like a study guide. This is crap for manifolds, there isn't really an origin - we have no (given) ambient Euclidean space
  4 KB (790 words) - 22:25, 12 April 2015
• Differential of a smooth map
  * Two [[Smooth manifold|smooth manifolds]] {{M|(M,\mathcal{A})}} and {{M|(N,\mathcal{B})}} (which may have different ...ed the '''differential of {{M|F}} at {{M|p}}'''<ref>Introduction to smooth manifolds - John M Lee - Second Edition</ref> as
  886 B (158 words) - 20:58, 13 April 2015
• Passing to the quotient (function)
  ...opology)]] which is defined by Mond (2013, Topology) and Lee (Intro to Top manifolds), by further abstracting the claim</ref>:
  8 KB (1,644 words) - 20:49, 11 October 2016
• Notes:Spherical coordinates
  ==Manifolds==
  10 KB (1,899 words) - 18:48, 23 September 2015
• Classes of continuously differentiable functions
  We may say {{M|f}} is<ref name="ITSM">Introduction to Smooth Manifolds - John M. Lee - Second Edition - Springer GTM</ref>: {{Definition|Real Analysis|Manifolds|Differential Geometry|Measure Theory}}
  3 KB (632 words) - 20:32, 16 October 2015
• Class of smooth real-valued functions on R-n
  ...]] on {{M|\mathbb{R}^n}} is denoted<ref name="ITSM">Introduction to Smooth Manifolds - John M. Lee - Second Edition</ref>: {{Definition|Manifolds|Functional Analysis|Real Analysis|Measure Theory}}
  2 KB (259 words) - 23:41, 21 October 2015