November 15th, 2016, 07:13 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 70 Thanks: 0  Compactness
Anyone??

November 17th, 2016, 04:22 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 357 Thanks: 196 Math Focus: Dynamical systems, analytic function theory, numerics 
Suppose not. Then you can find a sequence of values for $f$ such that for any open set, infinitely many values are not contained inside the set. Can you construct this sequence so that it has no convergent subsequence?


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