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May 12th, 2013, 04:41 AM  #1 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Functions of many variables
1. Find all limit points of sets in : 2. Check the existance (and calculate if possible) both limits of iterated functions in point for: , where is a Dirichlet function. 3. Judge if function for is continuous. Thank you. 
May 12th, 2013, 10:13 AM  #2 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: Some topology
sorry about the title, was thinking about something different and made a mistake.

May 12th, 2013, 10:15 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Some topology
To what would you like the title to be changed?

May 12th, 2013, 10:49 AM  #4 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: Some topology
Functions of many variables comes to my mind.

May 12th, 2013, 10:57 AM  #5  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Some topology Quote:
 
May 12th, 2013, 11:00 AM  #6 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: Functions of many variables
Thanks a lot.

May 12th, 2013, 03:17 PM  #7  
Senior Member Joined: Aug 2012 Posts: 2,209 Thanks: 651  Re: Functions of many variables Quote:
Can you do this problem in one dimension? What are the limit points in of  
May 12th, 2013, 11:37 PM  #8 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: Functions of many variables
It's obvious, but don't know how to prove obvious things.

May 12th, 2013, 11:45 PM  #9  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: Functions of many variables Quote:
Pardon the interuption, i have no idea how to proceed but your questions are fascinating...  
May 13th, 2013, 12:36 AM  #10 
Newbie Joined: Apr 2013 Posts: 11 Thanks: 0  Re: Functions of many variables
Okay, I've an idea: The sequence that converges to is a constant sequence if , else where gives first digits of 

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