Is a closed rectangle a 2d manifold with boundary? It seems like the corners don't have neighborhoods homeomorphic to the Euclidean half space?
2026-04-04 00:42:46.1775263366
Is rectangle manifold with boundary
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Summary of the comments: it is a topological manifold with boundary. It can be regarded as a smooth manifold with boundary, but then the embedding into $\mathbb{R}^2$ fails to be smooth. It can also be regarded as a smooth manifold with corners.