definition of vectors subbundle of rank \(k\) of vectors bundle of rank \(k'\)
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of vectors bundle of rank \(k\).
Target Context
- The reader will have a definition of vectors subbundle of rank \(k\) of vectors bundle of rank \(k'\).
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:
\( (E', T, \pi')\): \(\in \{\text{ the vectors bundles of rank } k'\}\)
\( E\): \(\subseteq E'\), with the subspace topology
\( \pi\): \(= \pi' \vert_{E}: E \to T\)
\( k\): \(\in \mathbb{N} \setminus \{0\}\) such that \(k \le k'\)
\(*(E, T, \pi)\): \(\in \{\text{ the vectors bundles of rank } k\}\)
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Conditions:
\(\forall t \in T (\pi^{-1} (t) \in \{\text{ the } k \text{ -dimensional vectors subspaces of } \pi'^{-1} (t)\})\)
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2: Note
This definition is not claiming that any \((E, T, \pi)\) that satisfies Conditions constitutes a vectors bundle; it is saying that if \((E, T, \pi)\) constitutes a vectors bundle with Conditions satisfied, it is called "vectors subbundle of \((E', T, \pi')\)"
