I study the book " Algebraic GeometryPart I: Schemes. With Examples and Exercises by Görtz, Wedhorn. " In order to give an example of a sublinear space of the projective space, they assum that $$l\colon\mathbb{P}^m_k\rightarrow\mathbb{P}^k_n$$ be the continuous map indiuced by the injective linear transformation $$\phi\colon k^{m+1}\rightarrow k^{n+1}$$ that maps $v$ to $A[v]$ where $A$ is the matrix accosiated with the linear map $\phi$. They say that
"This is infact an ismorphism of $\mathbb{P}^k_m$ to a closed subprevariety of $\mathbb{P}^n_k$." So I think that one needs to prove that $\text{Im}{l}$ is closed in $\mathbb{P}^k_n$. How I can prove that it is closed?