Comment by Gro-Tsen on Topological rigidity of cartesian product with $\mathbb{R}$

Let me just comment in passing that this isn't true without the “compact” hypothesis: if $V=\mathbb{R}^4$ and $W$ is an exotic $\mathbb{R}^4$, then $V\times\mathbb{R}$ and $W\times\mathbb{R}$ are both the standard $\mathbb{R}^5$.