1
$\begingroup$

The wedge sum of two circles has fixed point property?

I'm trying to find a continuous map from the wedge sum to itself, that this property fails, I couldn't find it, I need help.

Thanks

1 Answers 1

6

If by circle you mean $S^1$, and the fixed point property is the claim that every continuous map into itself has a fixed point, for two circles like so: enter image description here

consider the map that rotates $A$ by 90 degrees, and sends all of $B$ to the image of $x$.

  • 0
    yes, you're reason2012-11-29