799: C∞ Locally Trivial Surjection of Rank k

<The previous article in this series | The table of contents of this series | The next article in this series>

definition of $C^{\mathrm{\infty }}$ locally trivial surjection of rank $k$

---

Topics

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

---

The table of contents of this article

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

---

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 $C^{\mathrm{\infty }}$ manifolds with boundary.
• The reader knows a definition of Euclidean $C^{\mathrm{\infty }}$ manifold.
• The reader knows a definition of finite-product $C^{\mathrm{\infty }}$ manifold with boundary.

---

Target Context

• The reader will have a definition of $C^{\mathrm{\infty }}$ 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:
$M$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$E$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$k$: $\in \mathbb{N}\setminus \{0\}$
$\ast \pi$: $:E\to M$, $\in \{\text{ the locally trivial surjections of rank }k\}\cap \{\text{ the }{C}^{\mathrm{\infty }}\text{ maps }\}$
//

Conditions:
$\mathrm{\forall }\mathrm{\Phi }\in \{\text{ the local trivializations }\}(\mathrm{\Phi }\in \{\text{ the diffeomorphisms }\})$
//

${\mathbb{R}}^k$ and $U_m\times {\mathbb{R}}^k$ mentioned in a definition of locally trivial surjection of rank $k$ become the Euclidean $C^{\mathrm{\infty }}$ manifold and the product $C^{\mathrm{\infty }}$ manifold with boundary.

---

References

<The previous article in this series | The table of contents of this series | The next article in this series>