Focus Area 3: Topological connectivity and diameter of Discrete Structures In this paper we give the complete answer to a question posed by A. Arhangelʼskii and prove that the sphere S_n is diagonal resolvable if and only if S_n is an H-space if and only if n∈{0,1,3,7}. Moreover, we prove that any upper half even dimensional Q-sphere cannot be diagonal resolvable.