How would one go about proving ℝ(adsbygoogle = window.adsbygoogle || []).push({}); ^{n}is not homeomorphic to ℝ^{m}for m≠n. This isn't a homework question, I was told, but we weren't shown the proof.Is there somewhere with a proof I can see, or can someone outline it briefly?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

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!

# Not a homeomorphism R^n to R^m

Loading...

Similar Threads - homeomorphism | Date |
---|---|

I Homeomorphisms and ##\mathbb{R}## | Feb 22, 2018 |

I S^2 - {N} and R^2 homeomorphic? | Oct 6, 2017 |

I Why is this line not homeomorphic to the unit circle? | Sep 13, 2017 |

I Proving non homeomorphism between a closed interval & ##\mathbb{R}## | Jul 10, 2017 |

I Boundary and homeomorphism | May 21, 2017 |

**Physics Forums - The Fusion of Science and Community**