finite simplicial complex compact

Question

Let $K=(V,\Sigma)$ be a finite simplicial complex. I want to show that $|K|$ is compact. I know that $K$ is a sub-simplicial complex of $\Delta^V$ with $|\Delta^V|$ compact. So I think I should show that $|K| \subseteq |\Delta^V|$ is closed and therefore compact. But I have trouble understanding how a sub-simplicial complex translates into a sub-space. Thank you.