Convexity and Topology: Are They Related?

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Tomer
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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.
 
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I just realized it probably isn't :)
 
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