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Professor told me the two spaces are homeomorphic if we consider them as subspaces of R equipped with the standard topology.

It's a bit surprising for me since I have already found Q is homeomorphic to the positive rationals and I know that the two spaces in the main question are homeomorphic, so how can the positive rationals and non-negative rationals be homeomorphic?

hexaflexagonal
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tamefoxes
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  • It must have edited itself, I want a homeomorphism from the positive rationals to the non-negative rationals – tamefoxes Jul 15 '14 at 22:12
  • http://math.stackexchange.com/questions/119022/homeomorphism-between-mathbbq-and-mathbbq0-and-mathbbq-ge-0?rq=1 – Thomas Rot Jul 15 '14 at 22:28

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