Question: Prove Int(A) is an open set, given Int(A) is the set of all interior pts of A where x is an interior pt of A if it is the centre of an open ball in A.
The Attempt at a Solution
Attempted Soln: Suppose x is an element of Int(A).
Then there exists r > 0 such that B(x, r) is a subset of A.
Have tried to extend this to say there exists r > 0 such that B(x, r) is a subset of Int(A), but with no success.
Have also tried to prove C(Int(A)) contains all its limit pts and thus is closed. Then Int(A) would be open.
Just looking for a hint to get me on the right road. Thanks