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.

$\mathbb R^{v-1}$ is the set of all $v-1$-tuples of real numbers, i.e. all functions from
$\{1,2,\ldots, v-1\}$ to $\mathbb R$.  In the case $v=1$, that's all functions from the empty set to $\mathbb R$.  There is one function from the empty set to anything, namely a function that doesn't do anything.
I'd have to look closer at the paper you're referring to, to see what is done with $B$, but my guess is that the author didn't really bother much about the case $v=1$.  Either didn't think about it at all, or is leaving this up to the reader.
