779: Properly Embedded Submanifold with Boundary of 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 properly embedded submanifold with boundary of $C^{\mathrm{\infty }}$ manifold 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
• 2: Natural Language Description

---

Starting Context

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

---

Target Context

• The reader will have a definition of properly embedded submanifold with boundary of $C^{\mathrm{\infty }}$ 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: Structured Description

Here is the rules of Structured Description.

Entities:
$M^{\prime }$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$\ast M$: $\subseteq M^{\prime }$, $\in \{\text{ the embedded submanifolds with boundary }\}$
//

Conditions:
$\iota :M\to M^{\prime }\in \{\text{ the proper maps }\}$
//

---

2: Natural Language Description

For any $C^{\mathrm{\infty }}$ manifold with boundary, $M^{\prime }$, any embedded submanifold with boundary, $M\subseteq M^{\prime }$, such that the inclusion, $\iota :M\to M^{\prime }$, is a proper map

---

References

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