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PeterDonis said:I'm not sure this is a valid manifold, since it will include a boundary around the hole in the center and no coordinate chart is possible that can cover the boundary points.
A plane punctured by a single point would be a valid manifold since the single point left out does not preclude having a valid coordinate chart.
(Is there a restriction to use a single coordinate chart?)
Is an infinite-plane with a point removed
topologically equivalent to an infinite-plane with a disk and its disk-boundary removed?