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Re: Perplexing theorem
Posted:
Jun 19, 2000 1:46 AM


lmintz@mydeja.com wrote in message <8ik4p3$roc$1@nnrp1.deja.com>... >Theorem >Prove if is A dense in X and x(X then every neighborhood of x inter >sects A. > >Proof(kind of) > >Given a set X .C. R ,the set A .C. X is dense in X if every >point of X is a limit point of A or it is a point of A , >where '.C.' =subset of > >Let a(A and be an isolated point of A. Then a(A has a neighborhood >which contains no other points in A. Since A .C. X and A is dense in X >then a(X.But x(X in the neighboorhood of A. Then I guess it >intersects A?
I think you started this paragraph off wrong. You should say, "Let x(X and U be a neighborhood of x." Then see what happens if U does not intersect A in order to show that it must, which would prove the theorem.



