1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Closed subset of XxY?
  1. Closed subsets (Replies: 5)