Can every open set in $\mathbb{R}^n$ be subdivided into a simplicial complex?
Here, a simplicial complex $K$ must be a locally finite set of simplices in some $\mathbb{R}^m$ such that each face of a simplex in $K$ is also in $K$ and every non-empty intersection of simplices is in $K$.
I haven't been able to find any reference on this. I did see that the whole $\mathbb{R}^n$ can be subdivided into such a simplicial complex in several different ways (for instance, see Triangulations and Simplicial Methods by Chuangyin Dang). The only other question on this topic mentions Whitney's covering Lemma as a way to subdivide open sets of $\mathbb{R}^n$ using dyadic cubes, but I am not sure how these generate a locally finite simplicial subdivision.
If the answer is yes, I would greatly appreciate a reference for it.