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How to judge whether a space has the fixed-point property?

  1. Jul 27, 2010 #1
    I just learned the Brouwer fixed-point theorem of dimention 1 and 2.But the exercises make me sad,I can't solve them.

    Suppose X and Y are of the same homotopy type and X has the fixed-point property.Does Y also have it?
  2. jcsd
  3. Jul 27, 2010 #2


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    Have you tried coming up with some counterexamples? Find a space that you know has the fixed point theorem, find a homotopy equivalent space, and see if you can come up with a function without a fixed point. Either you'll end up getting the answer for free or you might come up with some intuition as to how the proof should go
  4. Jul 28, 2010 #3
    Yes,I've tried,but not very much.I will retry deep on it.Thank you
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