1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Restricted Jordan curve theorem

  1. Dec 11, 2007 #1
    1. The problem statement, all variables and given/known data

    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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook