Let V be a normed space, and S be the unit sphere in V:
S = {x ∈ V : ‖x‖ = 1}
Show that V is complete if and only if S is complete.
Let V be a normed space, and S be the unit sphere in V:
S = {x ∈ V : ‖x‖ = 1}
Show that V is complete if and only if S is complete.