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Topic: Perplexing theorem
Replies: 8   Last Post: Jun 23, 2000 1:41 PM

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Chuck Cadman

Posts: 16
Registered: 12/12/04
Re: Perplexing theorem
Posted: Jun 19, 2000 1:46 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply wrote in message <8ik4p3$roc$>...
>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.

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