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June 1st, 2012, 03:17 PM  #1 
Newbie Joined: May 2012 Posts: 14 Thanks: 0  Can you find a 4 ball contained in a 3 ball, with not equal?
In a metric space, an you find an open ball with radius 4, contained in an open ball with radius 3, but ? Why?

June 2nd, 2012, 01:10 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,607 Thanks: 616  Re: Can you find a 4 ball contained in a 3 ball, with not eq
Your question is confusing. How can you have a ball of radius 4 inside a ball of radius 3?

June 6th, 2012, 08:23 AM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Can you find a 4 ball contained in a 3 ball, with not eq
If A is an open ball with radius 4, then, given any , there exist points, p and q, in A such that . If , there is no ball of radius 3 containing both p and q.

June 7th, 2012, 11:13 PM  #4 
Senior Member Joined: Feb 2012 Posts: 144 Thanks: 16  Re: Can you find a 4 ball contained in a 3 ball, with not eq
let S={0,2,4} and let us use the usual distance. Then S is a metric space and B(2,3)=S B(0,4)={0,2} B(a,b) is the open ball with center a and radius b. 

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