How does one find a decreasing sequence of closed balls ( not necessarily concentric) in a complete metric space whose intersection is empty?
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1what do you mean "find"? do you just want one example? – MT_ Dec 30 '15 at 08:05
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Another example in an answer to An Example of a Nested Decreasing Sequence of Bounded Closed Sets with Empty Intersection – Dec 30 '15 at 08:06
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I am looking for a complete metric space and the radii of the closed balls may not decrease to zero. I don't see any such example in above posts. By 'find' I mean given an example. Apparently one can construct a metric on the natural numbers for which {n,n+1,n+2,...} is a closed ball for each n and the metric is complete. – Kavi Rama Murthy Jan 01 '16 at 04:19