reference request – Classification of limit points

Let $X$ be a subset of a topolgical space with no open points. Then
$$overline{X}=X_1sqcup X_2sqcup X_3sqcup X_4sqcup X_5$$
where $X_1$ are isolated points of $X$,
$X_2$ are interior points, $X_3=Xsetminus(X_1cup X_2)$, $X_4$ are isolated points of the complement of $X$ and
$X_5$ are none of the above.

Are there one-word English names for points in
$X_3,X_4,X_5$ or some unions of these sets which actually appeared in the literature? Recall that the points in $overline{X}$ are called adherent, $overline{X}setminus X_1$ are the limit points, and $overline{X}setminus X_2$ are the boundary points. But I do not know if there are names for other subsets (besides $X=X_1cup X_2cup X_3$).

(This should probably be Community Wiki.)