November 15th, 2016, 07:13 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 73 Thanks: 1  Compactness
Anyone??

November 17th, 2016, 04:22 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 470 Thanks: 261 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?


Tags 
compactness 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Proving compactness [unsolved]  boromir  Real Analysis  7  December 23rd, 2012 11:34 PM 
definable compactness  logi  Applied Math  0  May 9th, 2011 01:34 AM 
Compactness implies sequential compactness  guynamedluis  Real Analysis  6  April 21st, 2011 09:23 PM 
open covers and compactness  supermathman  Real Analysis  5  March 28th, 2009 10:16 PM 
Compactness  selinunan  Real Analysis  2  January 31st, 2009 08:42 AM 