## On dimension of algebraic sets February 9

Let $k$ be an algebraically closed field and $m\leq n$. Suppose $\pi:\mathbb{A}^n\to \mathbb{A}^m$ is map which sends $(a_1,\ldots,a_n)\to (a_1,\ldots,a_m)$. If $V$ is an affine algebraic set, then is it true that $\dim(V)\geq \dim(\overline{\pi(V)})