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Closed subset of XxY?

  1. May 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Let f:X->Y be a cts map from a topological space X to a Hausdorff space Y. Prove that the graph L={(x,y) in XxY: y=f(x)} is a closed subset of XxY.

    3. The attempt at a solution
    Hausdorff space are linked with open sets so how do you prove closeness in XxY?
  2. jcsd
  3. May 27, 2007 #2

    matt grime

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    This is not important but since open sets are linked to closed sets, then anything to do with closed sets has some relation with open sets. You understand that a set is open if and only if its complement is closed?

    So, start with L. What does it mean to be closed? There are many things to try, so write a few of them down and think about it for a while (perhaps a day or so, if need be - answers don't just magically appear instantly in people's minds).
  4. May 27, 2007 #3
    If only the assignment is not due tomorrow morning.:rolleyes:
  5. May 27, 2007 #4

    matt grime

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    L is closed if and only if its complement is open. Suppose that the complement is not open. What does that mean?
  6. Apr 25, 2010 #5
    Can you give more hint?

    Why can't we use the proof in Banach space in the following link?
    http://myyn.org/m/article/proof-of-closed-graph-theorem/ [Broken]
    Last edited by a moderator: May 4, 2017
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