October 31st, 2012, 06:51 AM  #1 
Newbie Joined: Oct 2012 From: Pakistan Gujranwala Posts: 9 Thanks: 0  Topology Give two examples of a complete metric space having two disjoint dense subsets 
October 31st, 2012, 09:58 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Topology
Hint: is dense in Can you think of a dense subset of that is disjoint from 
October 31st, 2012, 10:03 AM  #3 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  Re: Topology
One example is with the usual topology and rational numbers as a countable dense subset and irrational numbers also is dense subset, which are two disjoint dense subsets.

October 31st, 2012, 10:35 AM  #4 
Member Joined: Nov 2010 Posts: 48 Thanks: 0  Re: Topology
Also, the space is complete and the set of polynomial functions by Weierstrass theorem is dense. I'm not sure, but I think the set with trigonometric functions is also dense.

November 3rd, 2012, 09:41 PM  #5 
Newbie Joined: Oct 2012 From: Pakistan Gujranwala Posts: 9 Thanks: 0  Re: Topology thank you guys......... 

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