A definition of \(C^\infty\) manifold with boundary
Topics
About: \(C^\infty\) manifold
The table of contents of this article
Starting Context
- The reader knows a definition of topological manifold with boundary.
- The reader knows a definition of maximal atlas for topological manifold with boundary.
Target Context
- The reader will have a definition 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: Definition
Any topological manifold with boundary together with its any maximal atlas
2: Note
A \(C^\infty\) manifold with boundary may be a \(C^\infty\) manifold (without boundary), which in fact is a \(C^\infty\) manifold with empty boundary.
When we use the term, '\(C^\infty\) manifold with boundary', it always includes '\(C^\infty\) manifold (without boundary)'. When we specifically mean a \(C^\infty\) manifold with nonempty boundary, we will specifically state so.
