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smooth_manifold [2014/12/04 14:13] nikolaj |
smooth_manifold [2014/12/04 14:15] nikolaj |
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==== Discussion ==== | ==== Discussion ==== | ||
=== Elaboration === | === Elaboration === | ||
- | 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. | + | 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 defined as the biggest and hence //unique// one amongst those objects. |
=== Reference ==== | === Reference ==== |