My Math Forum Show the Annulus is polygonally path connected.
 User Name Remember Me? Password

 Complex Analysis Complex Analysis Math Forum

 January 26th, 2018, 04:45 AM #1 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 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: 905 Thanks: 351 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 Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post lu5t Real Analysis 2 November 29th, 2011 08:24 PM matthematical Real Analysis 4 October 5th, 2011 02:20 PM johnmath Real Analysis 5 May 18th, 2011 05:02 AM TTB3 Real Analysis 1 December 11th, 2009 03:55 PM cknapp Real Analysis 3 October 16th, 2009 02:41 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top