Given dynamic system $\dot x = Ax + Bu$, how can we prove that $M$ = {$(A,B)$: system is controllable} is an open set on an Euclidean space?

Question

I wish to show that $M$ = {$(A,B)$: system is controllable} is an open set in some Euclidean space. Equivalently, how can we show that the complement to this set is closed?

Here Controllability implies that $det[B, AB, A^2B, A^3B...A^{n-1}B] \neq 0$ where $A \in \mathbb{R}^{n \times n}$, and $B \in \mathbb{R}^{n \times 1}$

Can someone instruct me how to prove the pair $(A,B)$ forms an open set?