Let $X$ be a variety over a number field $K$. Let $S$ be a finite set of places of $K$. Is there a notion of a point $p \in X(\overline{K})$ to be "almost rational" in the following sense?:
$p$ and $^\sigma\!p$ are $v$-adically close for every $v\in S$ and $\sigma\in Gal(\overline{K}/K)$
I would like to know if this kind of notion is found anywhere in the literature and/or what is known about it.
