# 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?