Restricted Jordan curve theorem

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Homework Help Overview

The discussion revolves around the Restricted Jordan curve theorem, specifically a proof related to Lemma 2 found in a linked document. The original poster expresses confusion regarding the logical connection between two statements in the proof concerning nonintersecting segments and their relation to crossing the curve C.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand the reasoning behind a statement in the proof, questioning how the first sentence about nonintersecting segments leads to the conclusion about crossing the curve C. Other participants inquire about access to the document and clarify its location within the text.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the proof and its implications. Some have noted access issues to the document, while others are attempting to provide context about the theorem itself.

Contextual Notes

There are constraints regarding access to the document, as some participants mention needing a university subscription to view the relevant material. This may impact the depth of understanding and discussion regarding the theorem.

ehrenfest
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Homework Statement


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.


Homework Equations





The Attempt at a Solution

 
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I could not get to Lemma 2, only the abstract.
 
What do you mean? It is on the top of page 6.
 
You probably need a subscription to access that page (and such a subscription would likely be available through a university connection).
 
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.
 
anyone?
 

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