502: Function over C∞ Manifold with Boundary

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

definition of function over $C^{\mathrm{\infty }}$ manifold with boundary

---

Topics

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

---

The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Definition
• 2: Note

---

Starting Context

• The reader knows a definition of $C^{\mathrm{\infty }}$ manifold with boundary.
• The reader knows a definition of map.

---

Target Context

• The reader will have a definition of function over $C^{\mathrm{\infty }}$ manifold 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: Definition

For any $C^{\mathrm{\infty }}$ manifold with boundary, $M$, any map, $f:M\to \mathbb{R}$

---

2: Note

The term, 'function', has the general meaning that means any relation such that each element of the domain has the unique corresponding element in the range, but just 'function' in the manifold-context usually means the definition by this article, not just a general function.

---

References

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