### Topology

Posted:

**Wed Oct 31, 2012 10:00 am**Give two examples of a complete metric space having two disjoint dense subsets

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Posted: **Wed Oct 31, 2012 10:00 am**

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

Posted: **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 ?

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 ?

Posted: **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.

Posted: **Wed Nov 14, 2012 1:42 am**

yes give me

Posted: **Sat Aug 16, 2014 5:36 pm**

What about the algebraic and tracsendent real numbers in R?