We prove that an approximatively compact Chebyshev set in an M-space is a ?-sun and a ?-sun in a complete strong M-space (or externally convex M-space) is almost convex.

Some new continuity concepts called Outer Radially Lower(ORL), Outer Radially Upper (ORU) and Inner Radially Lower (IRL), for set-valued metric projections were introduced in Banach spaces by B. Brosowski and F. Deutsch [Bull. Amer. Math. Soc. 78(1972), 974-978] to characterize suns and Chebyshev sets. In this paper we extend these concepts together with the concept of Inner Radially Upper (IRU) continuity to convex metric spaces and prove some results including those of Brosowski and Deutsch in such spaces.