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

  • Thread starter kakarotyjn
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  • #1
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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?
 

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  • #2
Office_Shredder
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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
 
  • #3
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Yes,I've tried,but not very much.I will retry deep on it.Thank you
 

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