definition of \(C^\infty\) locally trivial surjection of rank \(k\)
Topics
About: \(C^\infty\) manifold
The table of contents of this article
Starting Context
- The reader knows a definition of locally trivial surjection of rank \(k\).
- The reader knows a definition of diffeomorphism between arbitrary subsets of \(C^\infty\) manifolds with boundary.
- The reader knows a definition of Euclidean \(C^\infty\) manifold.
- The reader knows a definition of finite-product \(C^\infty\) manifold with boundary.
Target Context
- The reader will have a definition of \(C^\infty\) locally trivial surjection 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:
\( M\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\( E\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\( k\): \(\in \mathbb{N} \setminus \{0\}\)
\(*\pi\): \(: E \to M\), \(\in \{\text{ the locally trivial surjections of rank } k\} \cap \{\text{ the } C^\infty \text{ maps }\}\)
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Conditions:
\(\forall \Phi \in \{\text{ the local trivializations }\} (\Phi \in \{\text{ the diffeomorphisms }\})\)
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\(\mathbb{R}^k\) and \(U_m \times \mathbb{R}^k\) mentioned in a definition of locally trivial surjection of rank \(k\) become the Euclidean \(C^\infty\) manifold and the product \(C^\infty\) manifold with boundary.
