922: Global Differential of C∞ Map Between C∞ Manifolds with Boundary

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

definition of global differential of $C^{\mathrm{\infty }}$ map between $C^{\mathrm{\infty }}$ manifolds with boundary

---

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 $C^{\mathrm{\infty }}$ manifold with boundary.
• The reader knows a definition of differential of $C^{\mathrm{\infty }}$ map between $C^{\mathrm{\infty }}$ manifolds with boundary at point.
• The reader knows a definition of tangent vectors bundle over $C^{\mathrm{\infty }}$ manifold with boundary.

---

Target Context

• The reader will have a definition of global differential of $C^{\mathrm{\infty }}$ map between $C^{\mathrm{\infty }}$ manifolds with boundary.

---

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:
$M_1$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$M_2$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$f$: $:M_1\to M_2$, $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ maps }\}$
$(T{M}_1,M_1,{\pi }_1)$: $=\text{ the tangent vectors bundle }$
$(T{M}_2,M_2,{\pi }_2)$: $=\text{ the tangent vectors bundle }$
$\ast df$: $:T{M}_1\to T{M}_2,v\mapsto d{f}_{{\pi }_1(v)}v$
//

Conditions:
//

---

References

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