February 18th, 2009, 11:58 AM  #1 
Newbie Joined: Feb 2009 Posts: 1 Thanks: 0  Closed/Open sets
Hey guys. I'm stuck on a problem and I need some direction/help on how to solve it: Prove that a set U c M is open IFF none of its points are limits of its compliment. Thanks! 
February 18th, 2009, 03:58 PM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Closed/Open sets
Hint: A set is open iff for every point there exists an such that the ball yx<\varepsilon\}" /> lies entirely in U. 

Tags 
closed or open, sets 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Open and Closed Sets  kaybees17  Real Analysis  3  October 23rd, 2013 02:26 AM 
Open / Closed Sets  veronicak5678  Real Analysis  1  May 1st, 2012 12:22 PM 
Open and Closed Sets  veronicak5678  Real Analysis  4  April 19th, 2012 04:37 PM 
neither open nor closed sets  mizunoami  Real Analysis  3  November 30th, 2011 06:06 PM 
Closed and Open Sets in R^d  x_saved_kt  Real Analysis  1  September 5th, 2011 01:24 PM 