A definition of tangent vector
Topics
About: \(C^\infty\) manifold with boundary
The table of contents of this article
Starting Context
- The reader knows a definition of \(C^\infty\) manifold with boundary.
- The reader knows a definition of function over \(C^\infty\) manifold with boundary.
- The reader knows a definition of derivation at point of \(C^k\) functions.
Target Context
- The reader will have a definition of tangent vector.
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: Definition
For any \(C^\infty\) manifold with (possibly empty) boundary, \(M\), and any point, \(p \in M\), any derivation at \(p\) of \(C^\infty\) functions
2: Note
\(C^\infty\) manifold with boundary, not just topological manifold with boundary, is required, because \(C^\infty\)-ness of function requires \(C^\infty\) manifold with boundary.
