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smooth_manifold [2014/12/04 14:11] nikolaj |
smooth_manifold [2014/12/04 14:13] nikolaj |
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| ==== Discussion ==== | ==== Discussion ==== | ||
| === Elaboration === | === Elaboration === | ||
| - | Effectively, a smooth manifold is given by providing any atlas. Due to the redundancy of some charts on small open sets, different atlases give rise to equivalent mathematical objects and so a smooth manifold is defined as the //unique// one with the biggest atlas. | + | Effectively, a smooth manifold would be given by providing //any// atlas. But then, due to the redundancy of some charts on small open sets, different atlases give rise to equivalent mathematical objects and so a smooth manifold is technically defined as the biggest and hence //unique// one amongst those objects. |
| === Reference ==== | === Reference ==== | ||
