Assignment:
In Rn with the usual topology, let A be the set of points x = (x1 , x2 .....xn) such that x12 + x22 + .....+xn2 ≤ 1. Prove that Bdry(A) is the (n-1)-dimensional sphere sn-1 , i.e., x Bdry(A) iff x12 + x22 + .....+xn2 = 1.
Provide complete and step by step solution for the question and show calculations and use formulas.