A conjecture implying the existence of non-convex Chebyshev sets in infinite-dimensional Hilbert spaces

In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space

Well posed optimization problems and nonconvex Chebyshev sets in Hilbert spaces

A result on the existence and uniqueness of metric projection for certain sets is proved, by means of a saddle point theorem. A conjecture, based on such a result and aiming for the construction of a nonconvex Chebyshev set in a Hilbert space, is presented