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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

Loading...

Similar Threads for metric space rationals |
---|

A How to Convert a Complex Logarithm to a Complex Exponential |

I Vector spaces and subspaces |

**Physics Forums | Science Articles, Homework Help, Discussion**