485: C∞ Manifold with Boundary

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

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Topics

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

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The table of contents of this article

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

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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.

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Target Context

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

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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.

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Main Body

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1: Definition

Any topological manifold with boundary together with its any maximal atlas

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2: Note

A $C^{\mathrm{\infty }}$ manifold with boundary may be a $C^{\mathrm{\infty }}$ manifold (without boundary), which in fact is a $C^{\mathrm{\infty }}$ manifold with empty boundary.

When we use the term, '$C^{\mathrm{\infty }}$ manifold with boundary', it always includes '$C^{\mathrm{\infty }}$ manifold (without boundary)'. When we specifically mean a $C^{\mathrm{\infty }}$ manifold with nonempty boundary, we will specifically state so.

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References

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