
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 26th, 2018, 04:45 AM  #1 
Senior Member Joined: Jan 2016 From: Blackpool Posts: 100 Thanks: 2  Show the Annulus is polygonally path connected.
Hello, I am asked to show that the annulus A(0,r,R) is polygonally path connected. For this question could i just give one specific example where i find points $w,z$in$U$ there are points $z=z_{0},z_{1},...z_{n}$=w where these points are contained inside the annulus? For example i could give a vector rotated by 2pi/n for n lots of z(points) For the second part of the question i am asked to give a sketch of my points to show intuitively that it is polygonally path connected. Thanks very much 
January 26th, 2018, 07:33 AM  #2 
Senior Member Joined: Oct 2009 Posts: 627 Thanks: 190 
Showing that an annulus is path connected is trivial. Now try to show in general for an open subset of $\mathbb{R}^n$ that path connected is the same as polygonally connected. Do this by creating balls inside the open subset. A ball is convex. 

Tags 
annulus, connected, path, polygonally, show 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Show that I^n and S^n are pathconnected?  lu5t  Real Analysis  2  November 29th, 2011 08:24 PM 
Path Connected Set?  matthematical  Real Analysis  4  October 5th, 2011 02:20 PM 
If X,Y are pathconnected spaces, and f:X>Y is a surjectio  johnmath  Real Analysis  5  May 18th, 2011 05:02 AM 
pathconnected  TTB3  Real Analysis  1  December 11th, 2009 03:55 PM 
Locally path connected space.  cknapp  Real Analysis  3  October 16th, 2009 02:41 PM 