- #1
kingwinner
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Homework Statement
Give an example of a decreasing sequence of closed balls in a COMPLETE metric space with empty intersection.
Hint 1: use a metric on N topologically equivalent to the discrete metric so that {n≥k} are closed balls.
Hint 2: In={n,n+1,n+2,...}. Consider the metric d(m,n)=∑1/2k where the sum is from k=m to k=n-1.
Homework Equations
N/A
The Attempt at a Solution
I really have no idea how to do this problem...how can we construct an example that would work?
Any help/hints is greatly appreciated!