My Math Forum Topology

 Topology Topology Math Forum

March 23rd, 2018, 11:08 AM   #1
Banned Camp

Joined: Dec 2017
From: Tel Aviv

Posts: 87
Thanks: 3

Topology

Is this picture show if the "inside & outside" is defined in topology?
Or this example isn't good?
Attached Images
 פניםחוץ.jpg (11.1 KB, 0 views)

March 23rd, 2018, 11:11 AM   #2
Banned Camp

Joined: Dec 2017
From: Tel Aviv

Posts: 87
Thanks: 3

topology picture

Is this picture better than the above?
And the picture above is wrong?
Attached Images
 פניםחוץ2.jpg (13.8 KB, 0 views)

 March 23rd, 2018, 12:36 PM #3 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,643 Thanks: 571 Math Focus: Yet to find out. I’m not sure what you’re asking. But you might like to look at the Jordan curve theorem. It turns out to be quite a subtle thing to define exactly what ‘inside’ and ‘outside’ mean. Thanks from policer
 March 23rd, 2018, 12:54 PM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,643 Thanks: 571 Math Focus: Yet to find out. A nice little explanation from a time when people actually bothered. Thanks from topsquark
 March 23rd, 2018, 01:16 PM #5 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 I have now read the definition of Jordan curve theorem. Jordan curve theorem is curve in a plain that not intersect itself and close (the ending point is also the starting point). So the first isn't a Jordan curve and the second it is a Jordan curve. Last edited by policer; March 23rd, 2018 at 01:19 PM.
March 23rd, 2018, 01:31 PM   #6
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,643
Thanks: 571

Math Focus: Yet to find out.
Quote:
 Originally Posted by policer I have now read the definition of Jordan curve theorem. Jordan curve theorem is curve in a plain that not intersect itself and close (the ending point is also the starting point). So the first isn't a Jordan curve and the second it is a Jordan curve.
That's right. Topologically, any figure equivalent to the circle is a Jordan curve. If you want, you can try prove the Jordan curve theorem using the intermediate value theorem for say, $|x| + |y| = 1$.

 March 23rd, 2018, 01:35 PM #7 Banned Camp   Joined: Dec 2017 From: Tel Aviv Posts: 87 Thanks: 3 Can you give more directions and hints: How to prove the intermediate value theorem for: |x|+|y|=1. I need a some directions...
March 23rd, 2018, 04:35 PM   #8
Senior Member

Joined: Sep 2016
From: USA

Posts: 444
Thanks: 254

Math Focus: Dynamical systems, analytic function theory, numerics
Quote:
 Originally Posted by policer Can you give more directions and hints: How to prove the intermediate value theorem for: |x|+|y|=1. I need a some directions...
As stated this does not make sense. The intermediate value theorem says that if $X$ is a connected topological space and $f: X \to \mathbb{R}$ is continuous, then $f(X)$ is an interval.

This does not seem to have anything to do with what you are asking about in this thread.

March 23rd, 2018, 05:01 PM   #9
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,643
Thanks: 571

Math Focus: Yet to find out.
Quote:
 Originally Posted by SDK This does not seem to have anything to do with what you are asking about in this thread.
I was trying to provide an exercise with which the OP could prove the JCT for a special case using the IVT.

As for what exactly is being asked in the thread, I've no idea.

 Tags topology

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Sammy2121 Topology 1 January 11th, 2015 07:02 PM vercammen Topology 1 October 19th, 2012 11:06 AM Artus Topology 5 September 5th, 2012 07:21 AM genoatopologist Topology 0 December 6th, 2008 10:09 AM Erdos32212 Topology 0 December 2nd, 2008 01:04 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top