819: Vectors Bundle of Rank k

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definition of vectors bundle of rank $k$

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Topics

About: topological space

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Note

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Starting Context

• The reader knows a definition of topological space.
• The reader knows a definition of locally trivial surjection of rank $k$.

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Target Context

• The reader will have a definition of vectors bundle of rank $k$.

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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: Structured Description

Here is the rules of Structured Description.

Entities:
$T$: $\in \{\text{ the topological spaces }\}$
$E$: $\in \{\text{ the topological spaces }\}$
$k$: $\in \mathbb{N}\setminus \{0\}$
$\pi$: $:E\to T$, $\in \{\text{ the locally trivial surjections of rank }k\}$
$\ast (E,T,\pi )$:
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Conditions:
//

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2: Note

This definition does not means that a $\pi$ exists for any arbitrary $T$ and $E$; it means that if a $\pi$ exists, $(E,T,\pi )$ is a vectors bundle.

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References

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