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October 31st, 2012, 05:51 AM   #1
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Topology

Give two examples of a complete metric space having two disjoint dense subsets
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October 31st, 2012, 08:58 AM   #2
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Re: Topology

Hint: is dense in Can you think of a dense subset of that is disjoint from
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October 31st, 2012, 09:03 AM   #3
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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.
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October 31st, 2012, 09:35 AM   #4
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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.
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November 3rd, 2012, 08:41 PM   #5
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Re: Topology

thank you guys.........
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