Restricted Jordan curve theorem

1. Dec 11, 2007

ehrenfest

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. Dec 11, 2007

EnumaElish

I could not get to Lemma 2, only the abstract.

3. Dec 11, 2007

ehrenfest

What do you mean? It is on the top of page 6.

4. Dec 11, 2007

morphism

You probably need a subscription to access that page (and such a subscription would likely be available through a university connection).

5. Dec 11, 2007

ehrenfest

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.

6. Dec 13, 2007

anyone?