Convergence of subsets of a complete geodesic space with curvature bounded above

We consider a notion of set-convergence in a Hadamard space recently defined by Kimura and extend it to that in a complete geodesic space with curvature bounded above by a positive number. We obtain its equivalent condition by using the corresponding sequence of metric projections. We also discuss the Kadec–Klee property on such spaces and interaction among this set-convergence having different curvatures.