 My Math Forum Show the Annulus is polygonally path connected.

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 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 Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded 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

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