(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Homework Help: Restricted Jordan curve theorem

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