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February 13th, 2017, 12:49 PM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 40 Thanks: 0  Prove limit point set is closed
Hi for this question my idea is too show that by the bolzanowaeirstrass theorem that there exists a convergent subsequence in the limitset Xnk that tends to Max{lim} so that subsequence converges to an element which is belongs to the limit point set.

February 13th, 2017, 01:55 PM  #2 
Senior Member Joined: Aug 2012 Posts: 1,428 Thanks: 352 
What makes you think there's a max? Also I didn't understand the notation Xnk. It would be more clear if you would write this problem carefully, defining your notation ("Let X be a metric space or a topological space or a set of reals," etc.), state exactly what you are being asked to prove, and writing down your argument step by step. Real analysis is as much to do with learning to write mathematics as it does with the actual content of the course. And one of the tricks to doing proofs is to write down explicitly what you are being asked to prove. By the time you do that, the proof usually suggests itself. 
February 13th, 2017, 02:34 PM  #3 
Senior Member Joined: Sep 2016 From: USA Posts: 114 Thanks: 45 Math Focus: Dynamical systems, analytic function theory, numerics  
February 14th, 2017, 01:57 AM  #4 
Member Joined: Jan 2016 From: Blackpool Posts: 40 Thanks: 0 
"prove that the limit point set is closed"


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