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Your understanding is fairly correct, but it is mathematically easier/nicer to tie the ends together rather than let them run to infinity. That guarantees that you describe exactly how the ends would 'continue forever', and fits better with topology.

See https://en.wikipedia.org/wiki/Knot_theory



Eh, putting a point at infinity (where the ends terminate) is hardly an obstacle to a mathematician. :)


- not all topologies have infinity.

- 'Continue forever' is vague. You will have to specify the direction, as that can affect the knot you get.


Ah. So much simpler, actually! Thanks.




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