Is there a natural topology on the set of open sets?

The interior Ǻ of a set A is the union of all open sets included in A?? Maths help?

• The interior Ǻ of a set A is the union of all open sets included in A a) prove that, for any set A, its interior Ǻ is open. b) prove that, for any set A, we have Ǻ ⊆ L(A) Please explain :)

• Answer:

  a) To prove this, we need to show that for any a in int(A), there is an open set S such that a is in S and S is a subset of int(A). Since int(A) is the union of a set of open sets, a in int(A) means that in particular a must be in some set in the union forming int(A). That would be the set S which we are looking for. The point A is in S, and S in a subset of int(A). b) Please explain what L(A) is. I don't recognize that notation.