I don't know if this is more appropriate for the topology forum, but I am learning this in analysis. I am asked to say whether or not(adsbygoogle = window.adsbygoogle || []).push({}); QandNare homeomorphic to eachother and to justify why. I am confused as to how to prove precisely that two spaces are homeomorphic, for there are no formal proofs of this in my text, only that (0,1] is not homeomorphic to the unit circle. everything else is just a visualisation of a donut and a coffee cup or something like that, but that doesn't really help me when thinking about N and Q. I know there exists a bijection, but I feel like it might not qualify for a homeomorphism because it doesn't necessarily send points that are close together or far away from eachother in N to points that are close together or far away in Q. I'm confused. Please help!

thanks

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# Is the metric space Q of rationals homeomorphic to N, the natural numbers?

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