Comments by "Zach B" (@zachb1706) on "Klein Bottles - Numberphile" video.

  1. Topology doesn’t care about shape. The shape of the Klein bottle is arbitrary, it can be stretched, shrunk, anything.
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  2. Going over what side? There is only one side. If you think of it like a 2D surface - the Klein bottle is only one 2D surface while the normal bottle has 2. Think about it, by your logic any strip of paper would have 1 side, as you can just go over the edge. But we know that only the Möbius strip does. In topology, volume and shape doesn’t really matter, the running joke is that topologists can’t tell the difference between a donut and a mug. Topologically they are the same thing.
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  3.  @alexawermuth1219  there is no edge topologically. We aren’t talking about edges in our normal view. Topology allows you to continuously change a shape and it still be the exact same shape. That’s how a donut is equal to a mug, and that’s why a Klein bottle has only one side
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  4.  @alexawermuth1219  there is no inside or outside. A bottle can be stretched and transformed into a flat disc. And vice versa. It doesn’t divide the world in 2.
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  5. 4 spacial dimensions
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  6. No
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