Let $k$ be an algebraically closed field and for positive integer $n$, consider the affine $n$-space $\mathbb A^n_k$ with Zariski topology. Consider $\mathbb A^m_k \times \mathbb A^n_k$ with product topology. Is there a good description of the irreducible closed subsets of the topological space $\mathbb A^m_k \times \mathbb A^n_k$ (possibly in terms of irreducible closed subsets of $\mathbb A^m_k, \mathbb A^n_k$) ?
I know that for irreducible subsets $X,Y$ of $\mathbb A^m_k, \mathbb A^n_k$ respectively, $X\times Y$ is irreducible in $\mathbb A^m_k \times \mathbb A^n_k$, but I don't know whether these are all irreducible closed subsets of $\mathbb A^m_k \times \mathbb A^n_k$ or not ...