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Let $X$ be a compact topological manifold with boundary. Suppose its interior is homeomorphic to $\mathbb{R}^n$. Is $X$ a (closed) ball?

Context: I want to show that some compactification of moduli of convex $n$-polygons (up to scaling and rotations) is a $(2n-4)$-cell. I can degenerate all sides (but $2$, of course), keeping records of the slopes, all angles to $\pi$ (again except $2$). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.

Let $X$ be a compact topological manifold with boundary. Suppose its interior is homeomorphic to $\mathbb{R}^n$. Is $X$ homeomorphic to a (closed) ball?

Context: I want to show that a certain compactification of moduli of convex $n$-polygons (up to scaling and rotations) is a $(2n-4)$-cell. I can degenerate all sides (but $2$, of course), keeping records of the slopes, and all angles to $\pi$ (again except $2$). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.

$X$ is a compact topological manifold with boundary. Its interior is homeomorphic to $\mathbb{R}^n$. Is $X$ a (closed) ball?

Context: I want to show that some compactification of moduli of convex $n$-polygons (upto scaling and rotations) is a $(2n-4)$-cell. I can degenerate all sides (but $2$, of course), keeping records of the slopes, all angles to $\pi$ (again except $2$). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.

Let $X$ be a compact topological manifold with boundary. Suppose its interior is homeomorphic to $\mathbb{R}^n$. Is $X$ a (closed) ball?

Context: I want to show that some compactification of moduli of convex $n$-polygons (up to scaling and rotations) is a $(2n-4)$-cell. I can degenerate all sides (but $2$, of course), keeping records of the slopes, all angles to $\pi$ (again except $2$). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.

X is a compact topological manifold with boundary. Its interior is homeomorphic to R^n. Is X a (closed) ball?

Context: I want to show that some compactification of moduli of convex n-polygons (upto scaling and rotations) is a (2n-4)-cell. I can degenerate all sides (but 2, of course), keeping records of the slopes, all angles to \pi (again except 2). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.

$X$ is a compact topological manifold with boundary. Its interior is homeomorphic to $\mathbb{R}^n$. Is $X$ a (closed) ball?

Context: I want to show that some compactification of moduli of convex $n$-polygons (upto scaling and rotations) is a $(2n-4)$-cell. I can degenerate all sides (but $2$, of course), keeping records of the slopes, all angles to $\pi$ (again except $2$). If more structure is needed, like smoothness on the interior, PL at the boundary - you have it.