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Aug 25, 2015 at 21:52 comment added John Harvey The point $p$ will be just be the limit of the $p_i$. I think it's easier to consider the compact case. The non-compact case then follows by repeatedly passing to subsequences as you increase the radius of the balls.
Aug 25, 2015 at 14:56 comment added Anton Petrunin Yes it is true and follow directly from the definition. However it is not true that the sequence can be found in the ultrafilter, see mathoverflow.net/questions/111842
Aug 25, 2015 at 12:07 history asked dg.jan CC BY-SA 3.0