Excuse me can you see my question
Let (X,T) be a topological space . Let H be the collection of closed sets in X . Let C be the collection of closed set satisfying every $$V \in H$$ is an intersection of element of C . Show that $$B={A^{c} : A \in C}$$ is a base for T ??

For the seconed condition that i take B1 And B2 in B s.t $$x \in B1 \cap B2$$ there exist $$B3=B1 \cap B2 $$s.t $$ x\in B3 \subset B1 \cap B2 $$

But i can not make the first condition << can you help me please