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Restricted Jordan curve theorem

  1. Dec 11, 2007 #1
    1. The problem statement, all variables and given/known data
    http://ieeexplore.ieee.org/iel5/9518/30166/01385873.pdf?arnumber=1385873

    I am reading a proof of the Restricted Jordan curve theorem (see Lemma 2 of the link) and the first two sentences are:

    "Because the list of segments is finite, nonintersecting segments cannot be arbitrarily close. Hence we can leave a face only by crossing C."

    I do not understand why the second sentence follows from the first.


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 11, 2007 #2

    EnumaElish

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    I could not get to Lemma 2, only the abstract.
     
  4. Dec 11, 2007 #3
    What do you mean? It is on the top of page 6.
     
  5. Dec 11, 2007 #4

    morphism

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    You probably need a subscription to access that page (and such a subscription would likely be available through a university connection).
     
  6. Dec 11, 2007 #5
    Oh yeah. I forgot about the university subscription thing.

    Restricted Jordan Curve Theorem: A simple closed polygonal curve C consisting of finite number of segments partitions the plane into exactly 2 faces, each have C as boundary.


    A polygonal curve is a curve composed of finitely many line segments.
     
  7. Dec 13, 2007 #6
    anyone?
     
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