Is there a common name for the complement $\widehat{X} \setminus X$ of a metric space $X$ in its metric completion $\widehat{X}$? Since $X$ is not necessarily open in $\widehat{X}$, the term *boundary* is out of the question (without additional qualifiers). *Metric remainder* seems appropriate but I did not find it in the literature.



Is there a common name for the complement of a metric space in its completion?
Remainder. I agree with that. But I don't find it on-line. Maybe "remainder" is primarily used for $\beta X \setminus X$ ? But it should be OK in your setting if you say the first time you use it: "the remainder of $X$ in its completion" or something.


