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June 1st, 2012, 04:17 PM   #1
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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?
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June 2nd, 2012, 02:10 PM   #2
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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?
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June 6th, 2012, 09:23 AM   #3
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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.
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June 8th, 2012, 12:13 AM   #4
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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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