definition of tangent vectors space at point
Topics
About: \(C^\infty\) manifold with boundary
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 tangent vector.
- The reader knows a definition of %field name% vectors space.
Target Context
- The reader will have a definition of tangent vectors space at point.
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:
\( M\): \(\in \{\text{ the } C^\infty \text{ manifolds with (possibly empty) boundary }\}\)
\( p\): \(\in M\)
\(*T_pM\): \(= \{\text{ the tangent vectors at } p\}\) with the vectors space structure
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Conditions:
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2: Natural Language Description
For any \(C^\infty\) manifold with (possibly empty) boundary, \(M\), and any point, \(p \in M\), the vectors space of all the tangent vectors at \(p\), denoted as \(T_pM\)
