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Rectangle question and closure of the interior?

  1. Sep 24, 2010 #1
    The question says:

    Show that if Q = [a1,b1]x...x[an,bn] is a rectangle, the Q equals the closure of Int Q.

    The definition of closure that I have is Cl(A) = int(A) U bd(A). So I'd like to show that Cl(int(Q)) = int(int(Q)) U bd(int(Q)).

    But this just seems to be obvious to me which just makes it hard to prove - I just don't know what to write. Any hints/ideas on how to prove this rigorously?


    I guess I'd have to show something like:

    Int(AxB) = Int(A)xInt(B)

    And then I guess, I'd make a claim that bd(int(Q)) = {a1,b1,...,an,bn} and prove this by showing that no other boundary points exist?

    Questions like this I always find hard.
    Last edited: Sep 24, 2010
  2. jcsd
  3. Sep 24, 2010 #2
    You are being asked to show that Q = Cl (IntQ)
    You know how to define Int and Bd, so write out the definitions explicitly (in set theory notation) to show that they coincide.
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