<![CDATA[Math Is Fun Forum / Baire's category theorem]]>2009-07-12T15:31:47ZFluxBBhttp://www.mathisfunforum.com/viewtopic.php?id=12318<![CDATA[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.]]>http://www.mathisfunforum.com/profile.php?id=21432009-07-12T15:31:47Zhttp://www.mathisfunforum.com/viewtopic.php?pid=115323#p115323<![CDATA[Baire's category theorem]]>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.