I'm trying to find if the following has the fixed point property:

Is it enough to show:

Let

so belongs to but

Thus, does not have the fixed point property.

Printable View

- May 2nd 2011, 01:15 PMMathSuckerFixed point property.
I'm trying to find if the following has the fixed point property:

Is it enough to show:

Let

so belongs to but

Thus, does not have the fixed point property. - May 2nd 2011, 01:35 PMAckbeet
Not sure I understand. Typically, you think of a function as having the fixed point property. What is your function f from S to S?

- May 2nd 2011, 03:11 PMDrexel28
- May 2nd 2011, 03:13 PMDrexel28
- May 3rd 2011, 10:50 AMMathSucker
- May 3rd 2011, 11:31 AMDeveno
then this would depend on the structure imposed on S. for example, if one is regarding S as a topological group, then sure, because then (1,0) has to be a fixed point. but if one is just regarding S as a topological space, then no, we can pick any rotation by an angle that is not an integral multiple of

- May 3rd 2011, 12:44 PMDrexel28
- May 3rd 2011, 12:47 PMMathSucker
Now that I look at it again, the question has it as

Does that change things? - May 3rd 2011, 12:52 PMDrexel28