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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I found this to be a rather interesting proof. Use Baire's category theorem to prove the following:

If

is a collection of open dense sets in a complete metric space , then is dense.Give a counter example to show that "open" is a required property, without using the axiom of choice.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Bump! I'll be posting the really cool solution to this problem by tonight unless someone tells me not to. So if you want to work on it, let me know.

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