How can we define $\mathbb{R}^0$? I'm reading a paper which asks to consider some box B $\subset \mathbb{R}^{v-1}$, for all $v\geq 1$. So for example, if we let $v=2, $ we would have that B $\subset \mathbb{R}$, so B would just be some interval $I$. I'm wondering what the case would be for $v=1$. Then we would be considering some box $B \subset \mathbb{R}^0$. I'm not sure what to make of this. Would it be empty...or just a singular point?
I can link the paper if its helpful. Thanks in advance.

The way I think of $\mathbb R^0$ is as a $0$-dimensional vector space, so it is a singleton $\{0\}$ consisting of the $0$ element.
