Let C0 be the set of all continuous functions from [a,b] to R Let A = { f C0: f(q) is irrational for all q Q} where Q is the set of rational numbers. The question is: Is A a thick subset of C0. EDIT: The answer I had here was very wrong
Last edited by southprkfan1; Mar 8th 2010 at 05:49 AM.
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Originally Posted by southprkfan1 Let C0 be the set of all continuous functions from [a,b] to R Let A = { f C0: f(q) is irrational for all q Q} where Q is the set of rational numbers. The question is: Is A a thick subset of C0. I said it is because if we let: Gj = { f C0: f(q) Br(p) where r = 1/j and p is irrational for all q Q} Then each Gj is open and dense and A = {j=1 to ] Gj so A is thick. ...thoughts? What does thick mean?
Originally Posted by Drexel28 What does thick mean? Right, I forgot some people use different terms. A set is thick in a metric space M if it the intersection of countably many open and dense sets in M. I believe it is also called a 2nd category set or something.
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