A 3-manifold is a space that locally looks like Euclidean 3-dimensional space

A 3-manifold is a space that locally looks like Euclidean 3-dimensional space.

A topological space X is a 3-manifold if it is a second-countable Hausdorff space and if every point in X has a neighbourhood that is homeomorphic to Euclidean 3-space.

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