Is $\Bbb R^n\times\Bbb R^n$ the domain of Minkowski distance $D(X,Y)=\|X-Y\|_p \quad \text{for all } X,Y\in\Bbb R^n.$ This post says the Minkowski distance,
$D(X,Y)=\|X-Y\|_p \quad \text{for all } X,Y\in\Bbb R^n$
has the domain $\Bbb R^n\times\Bbb R^n$, since it has two arguments.
I guess the domain may be still $\Bbb R^n$.

$D(X,Y)$ takes two argument vectors, $X$ and $Y$, which are both $\mathbb{R}^n$, and this makes the domain $\mathbb{R}^n \times \mathbb{R}^n$. If the domain was $\mathbb{R}^n$, it means you need $n$ inputs to execute the function, however $D(X,Y)$ needs $2n$ inputs.
