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I am trying to come up with one. I can see that if you reflect the two sided rings and project them onto any one side, you get the one sided ring.

However, I cannot think of a function that does not in a bijective manner. Should we be mapping the odd circles of the two sided to the even ones in the one sided?

Any ideas of a proof that shows that there is a homeomorphism?

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    When you say *usual Hawaiian ring*, do you mean the version that looks like nested figure $8$’s instead of nested circles?2012-11-15
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    yes. Sorry I should have been more specific. Yes, the two sided one looks like the figure 8, while the one sided one looks like nested circles.2012-11-16

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