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#1 2009-06-26 11:10:33
- Ricky
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Baire's category theorem
I found this to be a rather interesting proof. Use Baire's category theorem to prove the following:
If
Give a counter example to show that "open" is a required property, without using the axiom of choice.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
#2 2009-07-13 01:31:47
- Ricky
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Re: Baire's category theorem
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.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."