Convexity and Topology: Are They Related?

[Tomer]

Hello!
It's not really a homework problem, but it should be able to help me with something.
I was just wondering: if two sets are Homeomoprh (topologically), and one of them is convex, does it mean that the other one is convex as well?

Thanks a lot!

Tomer.

 

[Tomer]

I just realized it probably isn't :)