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Homework Help: Homeomorphism between the open sets of the circle and the open sets of real line

  1. Oct 14, 2012 #1
    I'm trying to prove the homeomorphism between the open intervals
    of the real line and the open sets
    of the circle with the induced topology of R^2.
    Notice that the open sets of the circle is the intersection between
    the open balls in R^2 and the circle itself.
    Anyone can help me?

    thank you.
  2. jcsd
  3. Oct 15, 2012 #2


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    Gold Member

    Can you name any bijections (not necessarily homeomorphisms) between [itex]\mathbb{R}[/itex] and the circle? Then we can check whether these are homeomorphisms, or if there's an obvious modification to make them so.
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