# Find a vector space and a set without Tschebyschev center.

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.

• I think you must first give as an hypothesis that $A$ is a bounded set – Jean Marie Jan 17 at 22:01