July 25th, 2007
Post solution related comments here!
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August 14th, 2007 at 9:51 pm
Claim 7 is wrong. Consider the Cantor Set as a counter-example and show that claim 8 is wrong, then deduce that claim 7 must be wrong as well.
In reality, one can only prove the following:
Given a family of open and disjoint sets, the following holds:
union[ boundary[Ai] ] “is a subset of” boundary[ union[Ai] ]
Perform
October 31st, 2007 at 6:06 pm
Is the definition of boundary correct? it seems it should be
bdy(A) is the set { x | for all e>0, (x-e,x+e) contains both a point from A and from R-A }.
October 31st, 2007 at 6:10 pm
You are of course right.
October 31st, 2007 at 6:56 pm
I agree with the poster above. The boundary of a union is not necessarily the union of the boundaries, and the Cantor set (well, its complement) is a good example. Claim 4 is not very constructive… the intersection of the irrationals with a fat Cantor set?