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- Thread starter Delong66
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In summary, the set D, which is a subset of R^2 with subspace topology, is not a manifold. It does not satisfy the requirement of having a neighborhood homeomorphic to an open subset of Euclidean space for every point. Additionally, removing the origin would result in 4 disconnected components, making it different from any surface or 1-manifold. However, if the origin is removed, it can be considered a topological manifold with 4 connected components, each being a 1-manifold and globally homeomorphic to the Reals.

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If you remove the origin, I believe it is a topological manifold.WWGD said:

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Indeed, 4 lines, each a 1-manifold, globally homeomorphic to the Reals. A manifold with 4 connected components.jbergman said:If you remove the origin, I believe it is a topological manifold.

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