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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 ?
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?