For sets A and B in a topological space X, the following hold:
(1) Cl(X-A)=X-Int(A)
(2) Int(A)∩ Int(B) =Int (A∩B)
Let then it means for any open set with we have that . But then there is not open set with so that (otherwise the intersection would be empty). Therefore, is not and interior point of , thus, . Conversely, let , this means and . But if it means for any open set so that we have that . Thus, for any open set with we see that which means lies on the closure of .