Hi, I'm in an intro topology course and need help proving these statements using balls.
1) Prove for any set S that Interior(S) = Complement of (Closure of S Complement)
2) Prove that if A ⊆ B then Interior(A) ⊆ Interior(B)
3) Prove that if A ⊆ B then Closure(B Complement) ⊆ Closure(A Complement)
Thanks a lot!