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clarifying the ambient
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Sam Nead
Sam Nead
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Let $M$ be a connected closed surface. Suppose $N$ is a connected closed surface embedded in the interior of $M \times (0,1)$$M \times [0,1]$ such that $N$ separates $M \times \{0\}$ and $M \times \{1\}$. Can we prove the region bounded by $M \times \{0\}$ and $N$ is homeomorphic to $M \times [0,1]$?

Let $M$ be a connected closed surface. Suppose $N$ is a connected closed surface embedded in $M \times (0,1)$ such that $N$ separates $M \times \{0\}$ and $M \times \{1\}$. Can we prove the region bounded by $M \times \{0\}$ and $N$ is homeomorphic to $M \times [0,1]$?

Let $M$ be a connected closed surface. Suppose $N$ is a connected closed surface embedded in the interior of $M \times [0,1]$ such that $N$ separates $M \times \{0\}$ and $M \times \{1\}$. Can we prove the region bounded by $M \times \{0\}$ and $N$ is homeomorphic to $M \times [0,1]$?

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Adterram
Adterram
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Surface in a product domain

Let $M$ be a connected closed surface. Suppose $N$ is a connected closed surface embedded in $M \times (0,1)$ such that $N$ separates $M \times \{0\}$ and $M \times \{1\}$. Can we prove the region bounded by $M \times \{0\}$ and $N$ is homeomorphic to $M \times [0,1]$?