Topology

Forum for the GRE subject test in mathematics.
johnny_01
Posts: 7
Joined: Wed Oct 31, 2012 9:17 am

Topology

Postby johnny_01 » Wed Oct 31, 2012 10:00 am

Give two examples of a complete metric space having two disjoint dense subsets

Nr
Posts: 96
Joined: Tue Jan 24, 2012 6:09 am

Re: Topology

Postby Nr » Wed Oct 31, 2012 10:46 am

What do you exactly mean by 2 examples ?

Well, one example could be R. It's clearly complete and it has disjoint dense subsets, namely Q and Qc (the complement of Q).

Do you want another example besides that one ?

colldood
Posts: 41
Joined: Wed Dec 01, 2010 11:45 pm

Re: Topology

Postby colldood » Wed Oct 31, 2012 6:49 pm

Example 2: R^2 with Q^2 and (Q^2)c. I can give you n more examples if you want, where n is a natural number.

johnny_01
Posts: 7
Joined: Wed Oct 31, 2012 9:17 am

Re: Topology

Postby johnny_01 » Wed Nov 14, 2012 1:42 am

yes give me

DDswife
Posts: 58
Joined: Thu Aug 14, 2014 5:29 pm

Re: Topology

Postby DDswife » Sat Aug 16, 2014 5:36 pm

What about the algebraic and tracsendent real numbers in R?




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