
#1
Nov407, 03:25 AM

P: 2,268

1. The problem statement, all variables and given/known data
What is the torus excluding a disc homeomorphic to? What is the boundary of a torus (excluding a disc)? 3. The attempt at a solution RP^2 X RP^2? As a guess. 



#2
Nov407, 05:39 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

Excluding a disk? You mean you slice a disk out of the torus? What's left is simply connected and looks to me like it is homeomorhic to a ball.




#3
Nov407, 03:15 PM

P: 2,268

Yes, slice out a disk. A torus is a surface so it hollow? A ball is a solid. The torus still has a hole in it. How can it be homeomorphic to a ball?
I'd say it is homeomorphic to a proper torous which is homeomorphic to what? 



#4
Nov407, 04:50 PM

P: 2,268

Topology question
What is the boundary of a torus excluding a disc?




#5
Nov407, 05:52 PM

Sci Advisor
HW Helper
P: 9,398

What is it homeorphic to? Infinitely many things, obviously. But I don't immediately see them as being interesting. Now, what is it homotopic to, there is an interesting question.
The boundary of a torus excluding a (closed) disc is obvious, surely. What do you think happens to an object without a boundary if we remove something like a disc? 


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