On the continuity of the best copositive approximation function

In this paper the author studies the continuity of the best copositive approximation function that maps C(Q) onto any of its finite dimensional Haar subspaces, when Q is any compact subset of the real numbers. In the case when M is a Z-subspace of C(Q), the author characterizes those f∈C(Q) at which the copositive metric projection is continuous. He also proves that the copositive metric projection as a function, is always discontinuous.