Hello everyone.

I am trying to prove that if $\displaystyle A \subseteq X$ is dense then for any open $\displaystyle T$ we have $\displaystyle T \subseteq Cl(A \cap T)$. I tried assuming not, and I arrive at the statement $\displaystyle t \in A^c$ and I can't see why that would be a contradiction.

Does anyone know of a good proof of this? Also, is it necessary that the T be open?