definition of chart on \(C^\infty\) manifold
Topics
About: \(C^\infty\) manifold
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of \(C^\infty\) manifold.
- The reader knows a definition of chart on topological manifold.
Target Context
- The reader will have a definition of chart on \(C^\infty\) manifold.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( M\): \(\in \{\text{ the } C^\infty \text{ manifolds }\}\)
\(*(U \subseteq M, \phi)\): \(\in \{\text{ the charts on the topological manifold, } M\}\)
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Conditions:
\((U \subseteq M, \phi)\): \(\in \text{ the maximal atlas of } M\)
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2: Natural Language Description
For any \(C^\infty\) manifold, \(M\), any chart on the topological manifold that (the chart) is an element of the maximal atlas, \((U \subseteq M, \phi)\)
