59: Tangent Vector

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A definition of tangent vector

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Topics

About: $C^{\mathrm{\infty }}$ manifold with boundary

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Definition
• 2: Note

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Starting Context

• The reader knows a definition of $C^{\mathrm{\infty }}$ manifold with boundary.
• The reader knows a definition of function over $C^{\mathrm{\infty }}$ manifold with boundary.
• The reader knows a definition of derivation at point of $C^k$ functions.

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Target Context

• The reader will have a definition of tangent vector.

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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.

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Main Body

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1: Definition

For any $C^{\mathrm{\infty }}$ manifold with (possibly empty) boundary, $M$, and any point, $p\in M$, any derivation at $p$ of $C^{\mathrm{\infty }}$ functions

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2: Note

$C^{\mathrm{\infty }}$ manifold with boundary, not just topological manifold with boundary, is required, because $C^{\mathrm{\infty }}$-ness of function requires $C^{\mathrm{\infty }}$ manifold with boundary.

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References

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