definition of properly embedded submanifold with boundary of \(C^\infty\) manifold with boundary
Topics
About: \(C^\infty\) 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 \(C^\infty\) manifold with boundary.
- The reader knows a definition of proper map.
- The reader knows a definition of \(C^\infty\) embedding.
Target Context
- The reader will have a definition of properly embedded submanifold with boundary of \(C^\infty\) 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:
\( M'\): \(\in \{\text{ the } C^\infty \text{ manifolds with boundary }\}\)
\(*M\): \(\subseteq M'\), \(\in \{\text{ the embedded submanifolds with boundary }\}\)
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Conditions:
\(\iota: M \to M' \in \{\text{ the proper maps }\}\)
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2: Natural Language Description
For any \(C^\infty\) manifold with boundary, \(M'\), any embedded submanifold with boundary, \(M \subseteq M'\), such that the inclusion, \(\iota: M \to M'\), is a proper map
