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Daniele Tampieri
Daniele Tampieri
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I'm looking for conditions that ensure the closure of an embedded manifold is a manifold with boundary.

The specific case I'm interested is as follows. Consider an oriented $C^1$ surface ${\cal S}$ in $R^3$$\Bbb R^3$ such that its closure is known to be a $C^0$ surface with boundary. Moreover, suppose we know that the normal to ${\cal S}$ has a continuous extension to the closure. Does this imply that the closure is a $C^1$ manifold with boundary?

I'm looking for conditions that ensure the closure of an embedded manifold is a manifold with boundary.

The specific case I'm interested is as follows. Consider an oriented $C^1$ surface ${\cal S}$ in $R^3$ such that its closure is known to be a $C^0$ surface with boundary. Moreover, suppose we know that the normal to ${\cal S}$ has a continuous extension to the closure. Does this imply that the closure is a $C^1$ manifold with boundary?

I'm looking for conditions that ensure the closure of an embedded manifold is a manifold with boundary.

The specific case I'm interested is as follows. Consider an oriented $C^1$ surface ${\cal S}$ in $\Bbb R^3$ such that its closure is known to be a $C^0$ surface with boundary. Moreover, suppose we know that the normal to ${\cal S}$ has a continuous extension to the closure. Does this imply that the closure is a $C^1$ manifold with boundary?

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Brian Seguin
Brian Seguin
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When is the closure of a manifold a manifold with boundary?

I'm looking for conditions that ensure the closure of an embedded manifold is a manifold with boundary.

The specific case I'm interested is as follows. Consider an oriented $C^1$ surface ${\cal S}$ in $R^3$ such that its closure is known to be a $C^0$ surface with boundary. Moreover, suppose we know that the normal to ${\cal S}$ has a continuous extension to the closure. Does this imply that the closure is a $C^1$ manifold with boundary?