1. The problem statement, all variables and given/known data Hi, This is my first post. I had a question regarding open/closed sets and subspace topology. Let A be a subset of a topological space X and give A the subspace topology. Prove that if a set C is closed then C= A intersect K for some closed subset K of X. 2. Relevant equations 3. The attempt at a solution I know that if C is closed then its compliment is open. I started by letting V be an open set in X and then (A/C) = A intersect V . From there I think it’s fair to assume X is an element of C which implies that x is an element of A intersect K. I just can’t seem to prove that C = A intersect K from the information given. I also can show that x is an element of A intersect K then X is an element of C but I don't know if that would help.