I have such exercise: Give example of a vector space G and its subset A such that the center of A does not exists.
By the Tschebyschev center we mean the center of the smallest ball containing A ( that ball's radius is called radius of set A).
I spent 2 hours on thinking and havent got it yet. I think it must be infinite dimentional vector space, otherwise center exists. I thought about spaces known from functional analysis like L1,l1,c,c0,c00, but was unable to find an example.
Thanks in advance for help.