# 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.)