780: Regular Domain of C∞ Manifold with Boundary

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definition of regular domain 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: Structured Description
• 2: Natural Language Description

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Starting Context

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

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Target Context

• The reader will have a definition of regular domain 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: Structured Description

Here is the rules of Structured Description.

Entities:
$M^{\prime }$: $\in \{\text{ the }{C}^{\mathrm{\infty }}\text{ manifolds with boundary }\}$
$\ast M$: $\subseteq M^{\prime }$, $\in \{\text{ the properly embedded submanifolds with boundary }\}$
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Conditions:
$dimM=dim{M}^{\prime }$
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2: Natural Language Description

For any $C^{\mathrm{\infty }}$ manifold with boundary, $M^{\prime }$, any properly embedded submanifold with boundary, $M$, such that $dimM=dim{M}^{\prime }$

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References

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