Let X be an affine variety over $\mathbb{C}$, and let $Y\subseteq X$ be a constructible set. It is very well-known that the Zariski closure of $Y$ is the same as the closure of $Y$ in the standard Euclidean topology inherited from the inclusion $X\subseteq \mathbb{C}^{n}$. I would like to know/learn to whom such result is due?
I once heard someone say that such result could be due to André Weil or Jean-Pierre Serre.
Thanks in advance by any reference.