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

  • Thread starter kakarotyjn
  • Start date
  • #1
kakarotyjn
98
0
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?
 

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
2021 Award
5,234
1,181
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
kakarotyjn
98
0
Yes,I've tried,but not very much.I will retry deep on it.Thank you
 

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

Replies
1
Views
737
Replies
4
Views
490
  • Last Post
Replies
3
Views
257
Replies
5
Views
548
Replies
35
Views
5K
Replies
26
Views
4K
Replies
5
Views
429
Replies
2
Views
257
  • Last Post
Replies
1
Views
877
  • Last Post
Replies
6
Views
2K
Top